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Discrete Mathematics, Algorithms and Applications
Number of Followers: 2  Hybrid journal (It can contain Open Access articles)ISSN (Print) 1793-8309 - ISSN (Online) 1793-8317 Published by World Scientific  [121 journals]
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- Strong chromatic indices of certain binary operations on graphs
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Authors: Vikram Srinivasan Thiru, S. Balaji
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The strong edge-coloring of a graph G is a proper edge coloring such that all edges adjacent to any given edge receive different colors. Such an assignment of colors defines color classes all of which are induced matchings. The minimum number of color classes required for such an assignment of colors is defined as the strong chromatic index of a graph G. In this article, we discuss the strong chromatic index of graphs obtained by the amalgamation of two graphs, the rooted product of two graphs and the corona product of two graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-09-23T07:00:00Z
DOI: 10.1142/S1793830923500738
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- [math]-[math]-group structures on digital objects and an answer to an open
problem-
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Authors: Sang-Eon Han
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The paper examines various properties of [math]-[math]-subgroup structures and addresses an open problem on the existence of topological group structures on the [math]-dimensional Khalimsky ([math]-, for brevity) topological space and Marcus–Wyse ([math]-, for short) topological plane. In particular, we obtain many types of totally [math]-disconnected or [math]-connected subgroups of a [math]-connected [math]-[math]-group. Besides, we prove that each of the [math]-dimensional [math]-topological space and the [math]-topological plane cannot be a typical topological group. Unlike an existence of a [math]-[math]-group structure of [math] (see Proposition 4.7), we prove that neither of [math] and [math] is a topological group, where [math] (respectively, [math]) is a simple closed [math]- (respectively, [math]-) topological curve with [math] elements in [math] (respectively, [math]) and the operation “∗” is a special kind of binary operation for establishing a group structure of each of [math] and [math]. Finally, given a [math]-[math]-group structure of [math], we find several types of [math]-[math]-subgroup structures of it (see Theorem 5.7).
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-09-23T07:00:00Z
DOI: 10.1142/S179383092350074X
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- Study of Boolean networks via matrices of support
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Authors: Yangjiang Wei, Yi Ming Zou
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we investigate the dynamics of Boolean networks by using their matrices of support. We derive properties about the transients, fixed points, and limit cycles. We also study the graph properties of the phase spaces of Boolean networks, and show how to use matrices of support to construct Boolean networks with prescribed dynamics.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-09-22T07:00:00Z
DOI: 10.1142/S1793830923500714
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- Locating fair domination in graphs
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Authors: V. Swaminathan, R. Sundareswaran, L. Muthusubramanian
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Graphs considered here are simple, finite and undirected. A graph is denoted by [math] and its vertex set by [math] and edge set by [math]. Many researchers were attracted by two concepts introduced in [P. J. Slater, Domination and location in acyclic graphs, Networks 17 (1987) 55–64; P. J. Slater, Dominating and reference sets in graphs, J. Math. Phys. Sci. 22 (1988) 445–455; Y. Caro, A. Hansberg and M. Henning, Fair domination in graphs, Discrete Math. 312 (2012) 2905–2914]. One is locating domination and the other is fair domination. A subset [math] of [math] is called a locating dominating set of [math] if for any [math] and both sets are non-empty. [math] is called a fair dominating set of [math] for any [math]. In this paper, both properties are combined and locating fair domination is studied.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-09-20T07:00:00Z
DOI: 10.1142/S1793830923500696
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- Linear hash functions and their applications to error detection and
correction-
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Authors: Boris Ryabko
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
We describe and explore so-called linear hash functions and show how they can be used to build error detection and correction codes. The method can be applied for different types of errors (for example, burst errors). When the method is applied to a model where the number of distorted letters is limited, the obtained estimate of its performance is slightly better than the known Varshamov–Gilbert bound. We also describe random code whose performance is close to the same boundary, but its construction is much simpler. The proposed error correction codes are close to those obtained in the theory of linear codes, but there are examples when the proposed algorithms are more efficient.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-09-16T07:00:00Z
DOI: 10.1142/S1793830923500702
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- Codes arising from directed strongly regular graphs with [math]
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Authors: Medha Itagi Huilgol, Grace Divya D’Souza
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The rank of adjacency matrix plays an important role in construction of linear codes from a directed strongly regular graph using different techniques, namely, code orthogonality, adjacency matrix determinant and adjacency matrix spectrum. The problem of computing the dimensions of such codes is an intriguing one. Several conjectures to determine the rank of adjacency matrix of a DSRG [math] over a finite field, keep researchers working in this area. To address the same to an extent, we have considered the problem of finding the rank over a finite field of the adjacency matrix of a DSRG [math] with [math], including some mixed Moore graphs and corresponding codes arising from them, in this paper.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-09-13T07:00:00Z
DOI: 10.1142/S1793830923500660
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- On the [math]-spectral radius of the [math]-uniform supertrees
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Authors: Chang Liu, Jianping Li
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a [math]-uniform hypergraph with vertex set [math] and edge set [math]. A connected and acyclic hypergraph is called a supertree. For [math], the [math]-spectral radius of [math] is the largest [math]-eigenvalue of [math], where [math] and [math] are the diagonal tensor of the degrees and the adjacency tensor of [math], respectively. In this paper, we determine the unique supertrees with maximum [math]-spectral radius among all [math]-uniform supertrees with [math] edges and independence number [math] for [math], among all [math]-uniform supertrees with given degree sequences, and among all [math]-uniform supertrees with [math] edges and matching number [math] for [math], respectively.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-09-06T07:00:00Z
DOI: 10.1142/S1793830923500672
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- Stability of certified domination upon edge addition
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Authors: P. Roushini Leely Pushpam, M. Kamalam, B. Mahavir
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A dominating set [math] of a graph [math] is said to be certified, if every vertex [math] has either 0 neighbors or at least two neighbors in [math]. The cardinality of a minimum certified dominating set of [math] is called the certified domination number of [math] and is denoted by [math]. A graph [math] is said to be [math]-[math] stable if for any two vertices [math] such that [math], we have [math]. In this paper, we provide upper bounds for the [math]-value of [math]-[math] stable graph. We also characterize the trees and unicyclic graphs that are [math]-[math] stable.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-09-05T07:00:00Z
DOI: 10.1142/S1793830923500684
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- The trace of uniform hypergraphs with application to Estrada index
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Authors: Yi-Zheng Fan, Jian Zheng, Ya Yang
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we investigate the traces of the adjacency tensor of uniform hypergraphs (simply called the traces of hypergraphs). We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned to their connected sub-hypergraphs, and present some perturbation results for the traces of a hypergraph when its structure is locally changed. As an application we determine the unique hypertree with maximum Estrada index among all hypertrees with perfect matchings and given number of edges, and the unique unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph with girth [math] and given number of edges.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-08-28T07:00:00Z
DOI: 10.1142/S1793830923500659
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- Unstable graphs and packing into fifth power
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Authors: Mohammad Alzohairi, Tarak Louleb, Mohamed Y. Sayar
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In a graph [math], a subset [math] of the vertex set [math] is a module (or interval, clan) of [math] if every vertex outside [math] is adjacent to all or none of [math]. The empty set, the singleton sets, and the full set of vertices are trivial modules. The graph [math] is indecomposable (or prime) if all its modules are trivial. If [math] is indecomposable, we say that an edge [math] of [math] is a removable edge if [math] is indecomposable (here [math]). The graph [math] is said to be unstable if it has no removable edges. For a positive integer [math], the [math]th power [math] of a graph [math] is the graph obtained from [math] by adding an edge between all pairs of vertices of [math] with distance at most [math]. A graph [math] of order [math] (i.e., [math]) is said to be [math]-placeable into [math], if [math] contains [math] edge-disjoint copies of [math]. In this paper, we answer a question, suggested by Boudabbous in a personal communication, concerning unstable graphs and packing into their fifth power as follows: First, we give a characterization of the unstable graphs which is deduced from the results given by Ehrenfeucht, Harju and Rozenberg (the theory of [math]-structures: a framework for decomposition and transformation of graphs). Second, we prove that every unstable graph [math] is [math]-placeable into [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-08-17T07:00:00Z
DOI: 10.1142/S1793830923500593
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- Injective-edge-coloring of planar graphs with girth restriction
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Authors: Yuehua Bu, Peng Wang, Hongguo Zhu
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A [math]-[math]-[math]-[math] [math] [math] [math] [math] is a mapping [math] such that [math] for any three consecutive edges [math],[math],[math] of a path or a [math]-cycle. [math][math] has a [math]-injective-edge-coloring[math] is called the [math]. In this paper, we prove that for planar graphs [math] with [math], (1)[math] if [math]; (2)[math] if [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-08-05T07:00:00Z
DOI: 10.1142/S1793830923500507
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- Enhanced power graphs of certain non-abelian groups
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Authors: Parveen, Sandeep Dalal, Jitender Kumar
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The enhanced power graph of a group [math] is a simple undirected graph with vertex set [math] and two vertices are adjacent if they belong to the same cyclic subgroup. In this paper, we obtain the Laplacian spectrum of the enhanced power graph of certain non-abelian groups, viz. semidihedral, dihedral and generalized quaternion. Also, we obtained the metric dimension and the resolving polynomial of the enhanced power graphs of these groups. At the final part of this paper, we study the distant properties and the detour distant properties, namely: closure, interior, distance degree sequence, eccentric subgraph of the enhanced power graph of semidihedral group, dihedral group and generalized quaternion group, respectively.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-08-05T07:00:00Z
DOI: 10.1142/S1793830923500635
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- Graph antimagic labeling: A survey
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Authors: Jingxiang Jin, Zhuojie Tu
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
An antimagic labeling of a simple graph [math] is a bijection [math] such that [math] for any two vertices [math] in [math]. We survey the results about antimagic labelings and other labelings motivated by antimagic labelings of graphs, and present some conjectures and open questions.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-22T07:00:00Z
DOI: 10.1142/S1793830923300023
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- Optimal strategies for the static black-peg AB game with two and
three pegs-
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Authors: Gerold Jäger, Frank Drewes
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The AB Game is a game similar to the popular game Mastermind. We study a version of this game called Static Black-Peg AB Game. It is played by two players, the codemaker and the codebreaker. The codemaker creates a so-called secret by placing a color from a set of [math] colors on each of [math] pegs, subject to the condition that every color is used at most once. The codebreaker tries to determine the secret by asking questions, where all questions are given at once and each question is a possible secret. As an answer the codemaker reveals the number of correctly placed colors for each of the questions. After that, the codebreaker only has one more try to determine the secret and thus to win the game. For given [math] and [math], our goal is to find the smallest number [math] of questions the codebreaker needs to win, regardless of the secret, and the corresponding list of questions, called a [math]-strategy. We present a [math]-strategy for [math] for all [math], and a [math]-strategy for [math] for all [math] and show the optimality of both strategies, i.e., we prove that no [math]-strategy for a smaller [math] exists.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-22T07:00:00Z
DOI: 10.1142/S1793830923500490
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- On the broadcast independence number of circulant graphs
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Authors: Abdelamin Laouar, Isma Bouchemakh, Éric Sopena
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
An independent broadcast on a graph [math] is a function [math] such that (i) [math] for every vertex [math], where [math] denotes the diameter of [math] and [math] the eccentricity of vertex [math], and (ii) [math] for every two distinct vertices [math] and [math] with [math]. The broadcast independence number [math] of [math] is then the maximum value of [math], taken over all independent broadcasts on [math]. We prove that every circulant graph of the form [math], [math], admits an optimal [math]-bounded independent broadcast, that is, an independent broadcast [math] satisfying [math] for every vertex [math], except when [math], or [math] and [math] is even. We then determine the broadcast independence number of various classes of such circulant graphs, and prove in particular that [math], except for [math], [math], or [math] with [math] and [math], where [math] denotes the independence number of [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-20T07:00:00Z
DOI: 10.1142/S1793830923500532
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- Minimal codewords: An application of relative four-weight codes
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Authors: B. Rega, A. Ramesh Babu
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Secret-sharing is a vital topic of cryptography and has widely used in information protection. One technique to the development of secret-sharing schemes is primarily based on error-correcting codes. In this paper, we determine the minimal codewords of relative four-weight codes and have the utility in the secret sharing schemes.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-20T07:00:00Z
DOI: 10.1142/S1793830923500623
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- Capacity-insensitive algorithms for online facility assignment problems on
a line-
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Authors: Tsubasa Harada, Toshiya Itoh, Shuichi Miyazaki
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In the online facility assignment problem [math], there exist [math] servers [math] on a metric space where each [math] has an integer capacity [math] and a request arrives one-by-one. The task of an online algorithm is to irrevocably match a current request with one of the servers with vacancies before the next request arrives. As special cases for [math], we consider [math] on a line, which is denoted by [math] and [math], where the latter is the case of [math] with equidistant servers. In this paper, we perform the competitive analysis for the above problems. As a natural generalization of the greedy algorithm grdy, we introduce a class of algorithms called MPFS (Most Preferred Free Servers) and show that any MPFS algorithm has the capacity-insensitive property, i.e., for any MPFS algorithm alg for [math], if alg is [math]-competitive when [math], then alg is [math]-competitive for general [math]. By applying the capacity-insensitive property of the greedy algorithm grdy, we derive the matching upper and lower bounds [math] on the competitive ratio of grdy for [math]. To investigate the capability of MPFS algorithms, we show that the competitive ratio of any MPFS algorithm alg for [math] is at least [math]. Then, we propose a new MPFS algorithm idas (Interior Division for Adjacent Servers) for [math] and show that the competitive ratio of idas for [math] is at most [math], i.e., idas for [math] is best possible in all the MPFS algorithms. We also give numerical experiments to investigate the performance of idas and grdy and show that idas performs better than grdy for distribution of request sequences with locality.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-19T07:00:00Z
DOI: 10.1142/S179383092350057X
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- 4-Total domination game critical graphs
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Authors: Chalermpong Worawannotai, Karnchana Charoensitthichai
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The total domination game is played on a simple graph [math] with no isolated vertices by two players, Dominator and Staller, who alternate choosing a vertex in [math]. Each chosen vertex totally dominates its neighbors. In this game, each chosen vertex must totally dominates at least one new vertex not totally dominated before. The game ends when all vertices in [math] are totally dominated. Dominator’s goal is to finish the game as soon as possible, and Staller’s goal is to prolong it as much as possible. The game total domination number is the number of chosen vertices when both players play optimally, denoted by [math] when Dominator starts the game and denoted by [math] when Staller starts the game. If a vertex [math] in [math] is declared to be already totally dominated, then we denote this graph by [math]. A total domination game critical graph is a graph [math] for which [math] holds for every vertex [math] in [math]. If [math], then [math] is called [math]-[math]-critical. In this work, we characterize some 4-[math]-critical graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-19T07:00:00Z
DOI: 10.1142/S1793830923500611
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- On strict-double-bound graphs and Cartesian products of paths and cycles
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Authors: Yoshimi Egawa, Kenjiro Ogawa, Kenta Ozeki, Satoshi Tagusari, Morimasa Tsuchiya
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
For a poset [math] the strict-double-bound graph ([math]) of [math] is the graph with the vertex set [math] such that [math] if and only if [math] and there exist [math] and [math] distinct from [math] and [math] such that [math] and [math] For a connected graph [math], the strict-double-bound number [math] is defined as [math], where [math] is the graph with [math] vertices and no edges. In this paper we deal with the strict-double-bound numbers of Cartesian products of graphs. We show that [math] for [math], [math] for [math], and [math] for [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-17T07:00:00Z
DOI: 10.1142/S1793830923500581
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- Domination-related parameters in middle graphs
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Authors: Kijung Kim
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The middle graph [math] of a graph [math] is the graph obtained by subdividing each edge of [math] exactly once and joining all these newly introduced vertices of adjacent edges of [math]. It is known that the decision problems for Italian domination number [math], [math]-rainbow domination number [math] and Roman domination number [math] are NP-complete. Recently, it was proved that [math] for a graph [math] of order [math]. In this paper, we continue to study several domination and domatic numbers in middle graphs. We also obtain closed formulas for domination, secure domination and total domination numbers in middle graphs of rooted product graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-12T07:00:00Z
DOI: 10.1142/S179383092350060X
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- The power-generalized [math]-Horadam sequences in different modules and a
new cryptographic method with these sequences-
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Authors: Çağla Çelemoğlu, Ayşe Nallı
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this study, unlike other power sequences, we define new ones in the integer and integer-valued polynomial module. We call these sequences the power-generalized [math]-Horadam sequence in the integer module and the power-generalized [math]-Horadam sequence in the integer-valued polynomial module. Using these sequences, we rebuild the ElGamal cryptosystem and then obtain a new cryptographic method by combining this and symmetric systems. We provide an encryption example where our method is applied. Finally, we see the advantages of the new cryptographic method when we compare the obtained new cryptographic method with some of the asymmetric cryptographic systems such as RSA and ElGamal. And we achieve that new cryptographic method that has more advantageous.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-07-05T07:00:00Z
DOI: 10.1142/S1793830923500556
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- Faster optimal ate pairings for cyclotomic sparse families of
pairing-friendly elliptic curves with embedding degrees [math]-
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Authors: Senegue Gomez Nyamsi, Emmanuel Fouotsa, Calvin Tcheka
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Nowadays, pairing-based cryptography researchers are looking for new parameters for standard security levels against the new number field sieve tower number field sieve algorithm. Recently, they have suggested new parameters for well-studied pairing-friendly curves with odd embedding degrees five and seven resistant to this attack. In this paper, we define optimal ate pairing on curves using sparse families with embedding degrees five and seven. We also provide details to perform the miller loop and the final exponentiation using addition chain process. Our theoretical results costs indicate that these families of curves offer the best performance in the computation of the optimal ate pairing at the 128-bit security level compared to Cocks–Pinch curves of embedding degrees five and seven. The improvement is about [math] and [math] faster than the optimal ate pairing previously computed on Cocks–Pinch curves of embedding degrees five and seven, respectively.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-30T07:00:00Z
DOI: 10.1142/S1793830923500544
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- A constructive proof of the Fulkerson–Ryser characterization of
digraphic sequences-
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Authors: Asish Mukhopadhyay, Daniel John
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Analogous to the Erdos–Gallai inequalities that give necessary and sufficient conditions for the existence of a graph on [math] vertices with prescribed vertex degrees, the Ryser–Fulkerson inequalities give necessary and sufficient conditions for the existence of a digraph on [math] vertices with prescribed indegrees and outdegrees of the vertices. In this note, we give a short constructive proof of the sufficiency of the Ryser–Fulkerson inequalities.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-30T07:00:00Z
DOI: 10.1142/S1793830923500568
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- Neighbor sum distinguishing total coloring of planar graphs with
restrained cycles-
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Authors: Hongjun Du, Huijuan Wang, Weili Wu
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Given a graph [math] and a proper total [math]-coloring [math]: [math], we call [math] neighbor sum distinguishing total coloring provided [math] for any [math] where [math] for any [math]. Neighbor sum distinguishing total coloring was first defined by Pilśniak and Woźniak. They conjectured [math] colors enable any graph [math] to admit such a coloring. The neighbor sum distinguishing total chromatic number [math] is the minimum integer where a graph is needed for this coloring. In this paper, we present two conclusions that [math] provided there are no 3-cycles adjacent to 4-cycles in a planar graph [math] with [math] without cut edges, and [math] provided there are no 4-cycles intersecting with 6-cycles in a planar graph [math] with [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-23T07:00:00Z
DOI: 10.1142/S1793830923500465
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- Recommender systems based on matrix factorization and the properties of
inferred social networks-
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Authors: Santiago Uribe, Carlos Ramirez, Jorge Finke
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Recommender Systems (RS) are a vital part of companies with an active participation on the web. These companies require strategies that allow them to take advantage of product ratings from users in order to provide future recommendations to other users. In the last decade, several algorithms have been developed for movie recommendation, with Matrix Factorization algorithm being one of the most popular algorithms. Our approach is to evaluate the performance of this recommendation algorithm in scenarios where underlying social networks, which characterize certain types of interactions between users, can be inferred. In particular, the MovieLens dataset is used, which consists of approximately 100,000 ratings by 671 users on 9066 movies, during the period from 29 March 1996 to 24 September 2018.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-17T07:00:00Z
DOI: 10.1142/S1793830923500520
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- The weighted Tower of Hanoi
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Authors: El-Mehdi Mehiri, Hacene Belbachir
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The weighted Tower of Hanoi problem is a new generalization of the classical Tower of Hanoi problem, where a move of a disc between two pegs [math] and [math] is weighted by a positive real [math]. This new problem generalizes the concept of finding the minimum number of moves to solve the Tower of Hanoi, to find a sequence of moves with the minimum total weight. We present an optimal dynamic algorithm to solve the weighted Tower of Hanoi problem, as well as some of its properties. We also show the link of this generalization to the Tower of Hanoi variants with restricted disc moves, and how this new problem can generalize the concept of restricting a disc move.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-16T07:00:00Z
DOI: 10.1142/S1793830923500519
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- The Italian domination numbers of some generalized
Sierpiński networks-
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Authors: Zhipeng Liang, Liyun Wu, Jinxia Yang
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
An Italian dominating function of a graph [math] with vertex set [math] is defined as a function [math], which satisfies the condition that for every [math] with [math], [math]. The weight of an Italian dominating function on [math] is the sum [math] and the Italian dominating number, and [math] indicates the minimum weight of an Italian dominating function [math]. In this paper, the structure of the generalized Sierpiński networks is investigated using the bounds of Italian domination number of graphs and the methods of mathematical induction and reduction to absurdity. Then, the Italian domination on the generalized Sierpiński networks [math] is obtained, where [math] denotes any special class of Path [math], Cycle [math], Wheel [math], Star [math], and complete bipartite graph [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-08T07:00:00Z
DOI: 10.1142/S1793830923500453
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- On distance-[math] locating and distance-[math] dominating sets in graphs
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Authors: Eunjeong Yi
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] and [math] be positive integers, and let [math] be a simple and connected graph with vertex set [math]. For [math], let [math] denote the length of an [math] geodesic in [math] and let [math]. Let [math]. A set [math] is a distance-[math] locating set of [math] if, for any distinct [math], there exists a vertex [math] such that [math], and the distance-[math] location number, [math], of [math] is the minimum cardinality among all distance-[math] locating sets of [math]. A set [math] is a distance-[math] dominating set of [math] if, for each vertex [math], there exists a vertex [math] such that [math], and the distance-[math] domination number, [math], of [math] is the minimum cardinality among all distance-[math] dominating sets of [math]. The [math]-location-domination number of [math], denoted by [math], is the minimum cardinality among all sets [math] such that [math] is both a distance-[math] locating set and a distance-[math] dominating set of [math]. For any connected graph [math] of order at least two, we show that [math], where [math]. We characterize connected graphs [math] satisfying [math] equals [math] and [math], respectively. We examine the relationship among [math], [math] and [math]; along the way, we show that [math] if [math]. We also show that there exist graphs [math] and [math] with [math] such that [math] can be arbitrarily large. Moreover, we examine some graph classes.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-06T07:00:00Z
DOI: 10.1142/S1793830923500477
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- On [math] spectrum of the zero-divisor graph of the ring [math]
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Authors: Mohammad Ashraf, M. R. Mozumder, M. Rashid, Nazim
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a commutative ring and [math] be its zero-divisors set. The zero-divisor graph of [math], denoted by [math], is an undirected graph with vertex set [math] and two distinct vertices [math] and [math] are adjacent if and only if [math]. In this paper, for [math] where [math] and [math] are primes [math] and [math] and [math] are positive integers, we calculate the [math] spectrum of the graphs [math]
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-05T07:00:00Z
DOI: 10.1142/S1793830923500362
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- Hybrid ideals in right regular LA-semigroups
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Authors: S. Meenakshi, V. Keerthika, G. Muhiuddin, B. Elavarasan
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In a right regular [math]-semigroup, the hybrid ideals, hybrid interior ideals, hybrid (1,2)-ideals, hybrid generalized bi-ideals, and hybrid quasi-ideals are all introduced in this work. A right regular [math]-semigroup has also been described in terms of its hybrid right and hybrid left ideals. Moreover, we obtain some equivalent conditions in terms of hybrid two-sided ideal, hybrid bi- (respectively, generalized bi-)ideal, hybrid quasi-ideal, hybrid interior ideal and hybrid [math]-ideal over right regular [math]-semigroups.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-05T07:00:00Z
DOI: 10.1142/S1793830923500404
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- Injective edge coloring of some standard graph products
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Authors: Priyamvada, B. S. Panda
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
An injective [math]-edge-coloring of a graph [math] is an assignment [math] of colors to the edges of [math] such that any two edges [math] and [math] receive distinct colors if there exists an edge [math] different from [math] and [math] such that [math] is incident on [math] and [math] is incident on [math]. The least number of colors required by any injective edge coloring of [math] is called the injective chromatic index of [math] and is denoted by [math]. In this paper, we give tight upper bounds of the injective chromatic index of various standard graph products and operations, including the Cartesian product, lexicographic product, corona product, edge corona product, join, subdivision and Mycielskian of a graph.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-05T07:00:00Z
DOI: 10.1142/S1793830923500416
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- Some new results on captive dominating sets in graphs
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Authors: S. K. Vaidya, H. D. Vadhel
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A dominating set [math] is said to be a captive dominating set of [math] if [math] has no isolated vertex ([math] is a total dominating set) and each vertex [math] is adjacent to at least one vertex in [math]. A captive dominating set [math] is said to be a minimal captive dominating set if no proper subset [math] of [math] is a captive dominating set. The minimum cardinality of a minimal captive dominating set of [math] is called the captive domination number of [math] which is denoted by [math]. In this paper, we have characterized some results, determine the values of the domination-related parameters for the graph and its splitting graph, relate captive domination and packing number of a graph, etc. We have also constructed graphs for which [math]
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-06-05T07:00:00Z
DOI: 10.1142/S1793830923500489
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- Normal category of principal left ideals of bands
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Authors: C. S. Preenu, A. R. Rajan
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The principal left ideals of a regular semigroup have been abstractly described by Nambooripad as normal categories. A semigroup [math] is said to be a band if [math] for all [math]. Since bands are regular semigroups, the category of principal left ideals is a normal category. This paper characterizes the normal categories which arise as categories of principal left ideals of bands.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-31T07:00:00Z
DOI: 10.1142/S1793830923500374
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- Monophonic pebbling number of some families of cycles
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Authors: A. Lourdusamy, I. Dhivviyanandam, S. Kither Iammal
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a simple connected graph. A configuration of pebbles is a function from [math] to a set of integers. Consider a configuration of pebbles on [math]. A pebbling move consists of removing two pebbles off a vertex and placing one on an adjacent vertex. The monophonic pebbling number of [math] is the smallest integer [math] from which we can put one pebble to a target using monophonic path through pebbling moves. The monophonic [math]-pebbling number of [math] is the smallest positive integer [math] such that from any configuration of [math] pebbles we can put [math] pebbles on a target using monophonic path. Here we discuss these concepts for families of cycles.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-31T07:00:00Z
DOI: 10.1142/S1793830923500386
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- Edge metric dimension and mixed metric dimension of a plane graph [math]
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Authors: Huige Shen, Jing Qu, Na Kang, Cong Lin
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a connected graph where [math] is the set of vertices of [math] and [math] is the set of edges of [math]. The distance from the vertex [math] to the edge [math] is given by [math]. A subset [math] is called an edge metric generator for [math] if for every two distinct edges [math], there exists a vertex [math] such that [math]. The edge metric generator with the minimum number of vertices is called an edge metric basis for [math] and the cardinality of the edge metric basis is called the edge metric dimension denoted by [math]. A subset [math] is called a mixed metric generator for [math] if for every two distinct elements [math], there exists a vertex [math] such that [math]. A mixed metric generator containing a minimum number of vertices is called a mixed metric basis for [math] and the cardinality of a mixed metric basis is called the mixed metric dimension denoted by [math]. In this paper, we study the edge metric dimension and the mixed metric dimension of a plane graph [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-31T07:00:00Z
DOI: 10.1142/S1793830923500398
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- Detour distance Laplacian matrices for signed networks
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Authors: K. Biju, K. Shahul Hameed, Fouzul Atik
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A signed network [math] with the underlying graph [math], used as a mathematical model for analyzing social networks, has each edge in [math] with a weight [math] or [math] assigned by the signature function [math]. In this paper, we deal with two types of Detour Distance Laplacian (DDL) matrices for signed networks. We characterize balance in signed social networks using these matrices and we compute the DDL spectrum of certain unbalanced signed networks, as balanced signed networks behave like unsigned ones.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-31T07:00:00Z
DOI: 10.1142/S1793830923500428
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- New bounds on the outer-independent total double Roman domination number
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Authors: S. M. Sheikholeslami, L. Volkmann
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A double Roman dominating function (DRDF) on a graph [math] is a function [math] satisfying (i) if [math] then there must be at least two neighbors assigned two under [math] or one neighbor [math] with [math]; and (ii) if [math] then [math] must be adjacent to a vertex [math] such that [math]. A DRDF is an outer-independent total double Roman dominating function (OITDRDF) on [math] if the set of vertices labeled [math] induces an edgeless subgraph and the subgraph induced by the vertices with a non-zero label has no isolated vertices. The weight of an OITDRDF is the sum of its function values over all vertices, and the outer-independent total Roman domination number [math] is the minimum weight of an OITDRDF on [math]. In this paper, we establish various bounds on [math]. In particular, we present Nordhaus–Gaddum-type inequalities for this parameter. Some of our results improve the previous results.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-31T07:00:00Z
DOI: 10.1142/S179383092350043X
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- On the cop number of Sierpinski-like graphs
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Authors: Nazlıcan Çakmak, Emrah Akyar
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this study, the cops and robber game is transferred to the Sierpinski graph, Sierpinski-like graphs [math] and [math], Sierpinski gasket graph [math], and generalized Sierpinski graphs [math] where [math] has an order four and [math]. We show that the cop number of these graphs is [math], excluding [math]. We also give a strategy for the cops to win.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-26T07:00:00Z
DOI: 10.1142/S1793830923500349
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- Some results on the super domination number of a graph
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Authors: Nima Ghanbari
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a simple graph. A dominating set of [math] is a subset [math] such that every vertex not in [math] is adjacent to at least one vertex in [math]. The cardinality of a smallest dominating set of [math], denoted by [math], is the domination number of [math]. A dominating set [math] is called a super dominating set of [math], if for every vertex [math], there exists [math] such that [math]. The cardinality of a smallest super dominating set of [math], denoted by [math], is the super domination number of [math]. In this paper, we study super domination number of some graph classes and present sharp bounds for some graph operations.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-26T07:00:00Z
DOI: 10.1142/S1793830923500441
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- Distance energy change of complete split graph due to edge deletion
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Authors: Subarsha Banerjee
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The distance energy of a connected graph [math] is the sum of absolute values of the eigenvalues of the distance matrix of [math]. In this paper, we study how the distance energy of the complete split graph [math] changes when an edge is deleted from it. The complete split graph [math] consists of a clique on [math] vertices and an independent set on [math] vertices in which each vertex of the clique is adjacent to each vertex of the independent set. We prove that the distance energy of the complete split graph [math] always increases when an edge is deleted from it.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-22T07:00:00Z
DOI: 10.1142/S1793830923500337
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- Graph distance measures based on Balaban indices
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Authors: Xiaoyun Lv, Bo Deng, Feng Fu
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Dehmer et al. [Interrelations of graph distance measures based on topological indices, PLoS One 9 (2014) e94985] explored the graph measures based on some topological indices and demonstrated some useful properties of them. In this work, we survey the graph measures based on the Balaban index of a graph, and prove some extremal properties on them for several classes of graphs. Moreover, through numerical calculation and comparison, we find the graph measures based on Balaban index of a graph behave better than that based on Randić index in some special cases.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-20T07:00:00Z
DOI: 10.1142/S1793830923500295
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- Some new 3-designs invariant under the groups [math] and [math]
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Authors: Ali Reza Rahimipour, Morteza Adeli
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we determine all simple block-transitive 3-designs on 65 points with block stabilizer of order greater than 2, admitting the 2-transitive action of the group [math]. As a result, we find 23 3-designs on 65 points that have [math] as an automorphism group. Also we construct four 3-([math]) designs for [math] and two 3-([math]) designs for [math]. All of these designs have [math] as the full automorphism group. Some of these designs are flag and anti-flag-transitive.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-17T07:00:00Z
DOI: 10.1142/S1793830923500350
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- Reliability measures in brother trees
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Authors: Remi Mariam Reji, R. Sundara Rajan
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The network components of interconnection networks are exposed to failures. But it is necessary that a network should not break down when such failures occur. Thus reliability and efficiency of interconnection networks have been the subject of extensive study in past years. The connectivity, wide diameter, Rabin number, and fault diameter of a network are used as measures of reliability and efficiency. In this paper, the [math]-wide diameter, [math]-Rabin number, and [math]-fault diameter of brother tree BT[math], [math] are obtained.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-12T07:00:00Z
DOI: 10.1142/S1793830923500283
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- Eternal feedback vertex sets: A new graph protection model using guards
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Authors: Nour Dyab, Mohammed Lalou, Hamamache Kheddouci
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Graph protection using mobile guards has received a lot of attention in the literature. It has been considered in different forms, including Eternal Dominating set, Eternal Independent set and Eternal Vertex Cover set. In this paper, we introduce and study two new models of graph protection, namely Eternal Feedback Vertex Sets (EFVS) and m-Eternal Feedback Vertex Sets (m-EFVS). Both models are based on an initial selection of a feedback vertex set (FVS), where a vertex in FVS can be replaced with a neighboring vertex such that the resulting set is a FVS too. We prove bounds for both the eternal and m-eternal feedback vertex numbers on, mainly, distance graphs, circulant graphs and grids. Also, we deduce other inequalities for both parameters on cycles, complete graphs and complete bipartite graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-12T07:00:00Z
DOI: 10.1142/S1793830923500301
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- Coset component signed graph of a group
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Authors: Javeria Amreen, Sudev Naduvath
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, the notion of a newly derived signed graph called a coset component graph, based on cosets of subgroups of a group is introduced. Let [math] be a group and [math] be its subgroup. Then, the coset component graph of [math] in [math], denoted by [math], is a simple graph with the vertex set consisting of elements of [math] and two vertices say, [math] are adjacent if either [math] or [math]. A coset component signed graph of [math] in [math] is a signed graph whose edges get the sign in accordance with their inclusion in the edge set of the corresponding coset component graph. The structure and important properties of the coset component signed graphs are determined in this paper.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-12T07:00:00Z
DOI: 10.1142/S1793830923500313
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- Strongly bi-conjugative Relation — A new element in the class of
bi-conjugative relations-
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Authors: Daniel Abraham Romano
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The concept of regular relations at sets and the concepts of some other relations derived from these, such as normal and conjugative relations, have been the subject of study by several researchers. The concepts of bi-conjugative relations, finite extension of bi-conjugative relations and weakly finite extension of bi-conjugative relations were introduced and analyzed by Romano. In this paper, as a continuation of previous research, the author introduces and analyzes the concept of strongly bi-conjugative relations and one of its finitely extension as a specific case of bi-conjugative relations.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-12T07:00:00Z
DOI: 10.1142/S1793830923500325
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- [math]-Dynamic chromatic number of subdivision-edge neighborhood corona of
certain graph families-
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Authors: K. Kalaiselvi, N. Mohanapriya, V. Aparna
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a simple connected graph consisting of n vertices and [math] edges. In a proper [math]-coloring, an [math]-dynamic coloring of a graph [math] is one in which each vertex’s neighbors are provided at least min [math] different colors. The [math]-dynamic chromatic number of graph [math], given as [math], is the minimal [math] such that the graph has [math]-dynamic [math] coloring of [math]. In this study, we combine a few common graphs to provide the [math]-dynamic coloring of the subdivision-edge neighborhood corona of path graph [math] and star graph [math]. These graphs include path graph [math], cycle graph [math], complete graph [math], star graph [math], and double star graph [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-05-09T07:00:00Z
DOI: 10.1142/S179383092350026X
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- Mixed metric dimension of some plane graphs
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Authors: Na Kang, Zhiquan Li, Lihang Hou, Jing Qu
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a finite undirected simple connected graph with vertex set [math] and edge set [math]. A vertex [math] resolves two elements (vertices or edges) [math] if [math]. A subset [math] of vertices in [math] is called a mixed metric generator for [math] if every two distinct elements (vertices and edges) of [math] are resolved by some vertices of [math]. The minimum cardinality of a mixed metric generator for [math] is called the mixed metric dimension and is denoted by [math]. In this paper, we study the mixed metric dimension for the plane graph of web graph [math] and convex polytope [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-04-29T07:00:00Z
DOI: 10.1142/S1793830923500258
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- Fractional local edge dimensions of a graph
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Authors: Nosheen Goshi, Sohail Zafar, Tabasam Rashid
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Metric-based parameters aided the study of the structural properties of graph network space like complexity, central tendency, connectivity, robustness, accessibility, and vulnerability. At the same time, these parameters played a pivotal role in rectifying problems in navigation, integer programming, optimization, pattern recognition and avoidance, combinatoric detection, backtracking in geographical routing, etc. In this paper, we considered the fractional edge dimension, a metric-based parameter in local environment by initiating the study of the fractional local edge dimensions of a graph (FLED). We define the aforesaid concept and give its bounds. We discussed the characterization problem for FLED equal to [math], the realization problem, and its relation with the fractional metric dimensions. We also calculated the FLED of the Petersen graph, Coxeter graph, the families of cycle, complete, wheel, grid and complete [math]-partite graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-04-28T07:00:00Z
DOI: 10.1142/S1793830923500246
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- A family of multicolor lights out games
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Authors: Luciana Ferman, Crista Arangala
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Traditional two-color lights out games and their solutions have been studied extensively. This paper focuses on the existence, or lack there of, of solutions in more general lights out games, which take on a prime number of color states. The result in this paper generalizes the existence of solutions in the family of lights out games on a [math] grid with [math]-colors where [math] and [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-04-27T07:00:00Z
DOI: 10.1142/S1793830923500234
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- Euler numbers and diametral paths in Fibonacci cubes, Lucas cubes and
alternate Lucas cubes-
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Authors: Ömer Eğeci̇oğlu, Eli̇f Saygi, Zülfükar Saygi
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The diameter of a graph is the maximum distance between pairs of vertices in the graph. A pair of vertices whose distance is equal to its diameter is called diametrically opposite vertices. The collection of shortest paths between diametrically opposite vertices is referred as diametral paths. In this work, we enumerate the number of diametral paths for Fibonacci cubes, Lucas cubes and alternate Lucas cubes. We present bijective proofs that show that these numbers are related to alternating permutations and are enumerated by Euler numbers.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-04-27T07:00:00Z
DOI: 10.1142/S1793830923500271
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- Cyclic base ordering of generalized Petersen graphs
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Authors: Xiaofeng Gu, William Zhang
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A cyclic base ordering (CBO) of a connected graph [math] is a cyclic ordering of [math] such that every cyclically consecutive [math] edge induces a spanning tree of [math]. The density of [math] is defined to be [math]; and [math] is uniformly dense if [math] for every connected subgraph [math] of [math]. It was conjectured by Kajitani, Ueno and Miyano that [math] has a CBO if and only if [math] is uniformly dense. In this paper, we study CBO of generalized Petersen graphs to support this conjecture, and we prove that [math] and [math] have CBO.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-04-07T07:00:00Z
DOI: 10.1142/S1793830923500192
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- On local antimagic chromatic number of cycle-related join graphs II
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Authors: Gee-Choon Lau, K. Premalatha, S. Arumugam, Wai Chee Shiu
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
An edge labeling of a graph [math] is said to be local antimagic if it is a bijection [math] such that for any pair of adjacent vertices [math] and [math], [math], where the induced vertex label of [math] is [math] ([math] is the set of edges incident to [math]). The local antimagic chromatic number of [math], denoted by [math], is the minimum number of distinct induced vertex labels over all local antimagic labelings of [math]. In this paper, several sufficient conditions to determine the local antimagic chromatic number of the join of graphs are obtained. We then determine the exact value of the local antimagic chromatic number of many join graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-04-07T07:00:00Z
DOI: 10.1142/S1793830923500222
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- A penalty decomposition algorithm for the extended mean–variance–CVaR
portfolio optimization problem-
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Authors: Abdelouahed Hamdi, Tahereh Khodamoradi, Maziar Salahi
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we study mean–variance–Conditional Value-at-Risk (CVaR) portfolio optimization problem with short selling, cardinality constraint and transaction costs. To tackle its mixed-integer quadratic optimization model for large number of scenarios, we take advantage of the penalty decomposition method (PDM). It needs solving a quadratic optimization problem and a mixed-integer linear program at each iteration, where the later one has explicit optimal solution. The convergence of PDM to a partial minimum of original problem is proved. Finally, numerical experiments using the S&P index for 2020 are conducted to evaluate efficiency of the proposed algorithm in terms of return, variance and CVaR gaps and CPU times.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-04-04T07:00:00Z
DOI: 10.1142/S1793830923500210
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- [math]-Polar cubic [math]([math] and [math])-ideals of [math]-algebras
-
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Authors: Ahsan Mahboob, G. Muhiuddin
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we apply the [math]-polar cubic structures on BCI-algebras. We first present the ideas of [math]-polar cubic [math]-ideals, [math]-polar cubic [math]-ideals and [math]-polar cubic [math]-ideals in BCI-algebras. Then we prove that [math]-polar cubic [math]([math] and [math])-ideals are [math]-polar cubic ideals, but the converse assertion is not true, and an example is provided in this support. We define the conditions under which [math]-polar cubic ideals coincide with [math]-polar cubic [math]([math] and [math])-ideals. The associated properties of [math]-polar cubic [math]-ideals, [math]-polar cubic [math]-ideals, and [math]-polar cubic [math]-ideals are also examined. Furthermore, we consider [math]-polar cubic [math]([math] and [math])-ideals in terms of [math]([math] and [math])-ideals of BCI-algebras.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-31T07:00:00Z
DOI: 10.1142/S1793830923500131
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- Coupon coloring of Kneser graph [math]
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Authors: Mehrnoosh Shadravan, Rajab Ali Borzooei
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Chen et al. [On coupon coloring of graphs, Discrete Appl. Math. 193 (2015) 94–101] had introduced the concept of coupon coloring for any graph with no isolated vertex. A [math]-coupon coloring of [math] is an assignment of colors from [math] to the vertices of [math] such that the neighborhood of every vertex of [math] contains vertices of all colors from [math]. The maximum [math] for which a [math]-coupon coloring exists is called the coupon coloring number of [math], and is denoted by [math]. In this paper, we determine the coupon coloring number of Kneser graphs [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-31T07:00:00Z
DOI: 10.1142/S1793830923500209
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- Edge-vertex domination on interval graphs
-
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Authors: Amita Samanta Adhya, Sukumar Mondal, Sambhu Charan Barman
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
For an undirected as well as connected graph [math], a node point [math] is edge-vertex dominated by an edge [math] if [math] is incident to [math] or [math] is incident to an adjacent edge of [math]. A set [math] is called an edge-vertex dominating set of [math] if every node point of [math] is edge-vertex dominated by at least one edge of [math]. The minimum cardinality among all edge-vertex dominating sets is the edge-vertex domination number, symbolled by [math]. Here, we propose an algorithm that runs in [math]-time for determining a minimum-cardinality [math] of interval graph with [math] nodes. We also study some properties relating to the edge-vertex dominating set of interval graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-28T07:00:00Z
DOI: 10.1142/S1793830923500155
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- The forcing geodetic global domination number of a graph
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Authors: V. Selvi, V. Sujin Flower
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a connected graph and [math] be a minimum geodetic global dominating set of [math]. A subset [math] is called a forcing subset for [math] if [math] is the unique minimum geodetic global dominating set containing [math]. A forcing subset for [math] of minimum cardinality is a minimum forcing subset of [math]. The forcing geodetic global domination number of [math], denoted by [math], is the cardinality of a minimum forcing subset of S. The forcing geodetic global domination number of [math], denoted by [math], is [math], where the minimum is taken over all minimum geodetic global dominating sets [math] in [math]. The forcing geodetic global domination number of some standard graphs are determined. Some of its general properties are studied. It is shown that for every pair of positive integers a and b with [math] and [math], there exists a connected graph [math] such that [math] and [math]. The geodetic global domination number of join of graphs is also studied. Connected graphs of order [math] with geodetic global domination number 2 are characterized. It is proved that, for a connected graph [math] with [math]. Then [math] and characterized connected graphs for which the lower and the upper bounds are sharp.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-28T07:00:00Z
DOI: 10.1142/S1793830923500167
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- Further results on (total) restrained Italian domination
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Authors: A. M. Ridha Abdulhasan, D. A. Mojdeh
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
An Italian dominating function on a graph [math] is defined as a function [math] satisfying the condition that every vertex [math] for which [math] is adjacent to at least one vertex [math] for which [math] or at least two vertices [math] for which [math]. The weight of an Italian dominating function is [math]. The Italian domination number is the minimum weight taken over all Italian dominating functions of [math] and denoted by [math]. Three domination parameters related to the Italian dominating function are total Italian, restrained Italian, and total restrained Italian dominating function. A total ((restrained) (total restrained)) Italian dominating function [math] is an Italian dominating function if the set of vertices with positive label ((the set of vertices with label [math]), (at the same time, the set of vertices with positive label and the set of vertices with label [math])) induces ((induces) (induce)) a subgraph with no isolated vertex. A minimum weight of any total ((restrained) (total restrained)) Italian dominating function [math] is called a total ((restrained) (total restrained)) Italian domination number denoted by [math], (([math]) ([math])). We initiate the study of parameters, restrained and total restrained Italian domination number of a graph [math] and the middle graph of [math]. For the family of standard graphs, we obtain the exact value of these parameters. For arbitrary graph [math], we obtain the sharp bounds of these parameters, and for some corona graphs, we establish the precise value of these parameters.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-25T07:00:00Z
DOI: 10.1142/S1793830923500179
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- [math]-Delaunay triangulation: A new efficient algorithm for merging two
adjacent Delaunay triangulations-
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Authors: Phan Thanh An, Trinh Minh Duc, Dang Thi Oanh
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we present an efficient algorithm, namely Orienting and Final Circles (OFC)-Delaunay Triangulation, for constructing the Delaunay triangulation of a finite planar point set using the idea of the Method of Orienting Curves (introduced by Phu in Zur Lösung einer regulären Aufgabenklasse der optimalen Steuerung im Groen mittels Orientierungskurven, Optimization 18(1) (1987) 65–81 and Ein konstruktives Lösungsverfahren für das Problem des Inpolygons kleinsten Umfangs von J. Steiner, Optimization 18(3) (1987) 349–359). The concepts of orienting and final circles are introduced. The Delaunay edges are determined by orienting circles and a final circle. Our algorithm has [math]([math]) worst-case running time. The algorithm is implemented in Python and some numerical examples are presented.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-22T07:00:00Z
DOI: 10.1142/S1793830923500143
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- Line graphs associated to Von Neumann regular graphs of rings
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Authors: Laithun Boro, Madan Mohan Singh
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a commutative ring with unity. Taloukolaei and Sahebi [Von Neumann regular graphs associated with rings, Discrete Math. Algorithms Appl. 10(3) (2018) 1850029, doi:10.1142/S1793830918500295] introduced the Von Neumann regular graph [math] of a ring [math] whose vertices are the elements of [math] and two distinct vertices [math] and [math] are adjacent if and only if [math] is a Von Neumann regular element of [math]. In this paper, we investigate and determine some graph theoretic properties of the line graph [math] associated to [math]. We give some characterization results regarding the completeness, bipartiteness, traversability, diameter and girth. We also prove Beck’s conjecture for [math]. Finally we characterize rings having the planarity, the outerplanarity and also being the ring graph of the line graphs associated to Von Neumann regular graphs [math] of rings.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-13T07:00:00Z
DOI: 10.1142/S1793830923500088
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- Solving the [math]-coloring problem for subdivision-edge neighborhood
coronas-
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Authors: Raúl M. Falcón, M. Venkatachalam, S. Julie Margaret
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, the [math]-coloring problem is solved for every subdivision-edge neighborhood corona of paths, cycles, stars and complete graphs. In addition, some exact values and sharp bounds are established for the [math]-chromatic number of subdivision-edge neighborhood coronas of these graphs with any other graph.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-13T07:00:00Z
DOI: 10.1142/S179383092350009X
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- Adjacency spectra of semigraphs
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Authors: Pralhad M. Shinde
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we define the adjacency matrix of a semigraph. We give the conditions for a matrix to be semigraphical and give an algorithm to construct a semigraph from the semigraphical matrices. We derive lower and upper bounds for largest eigenvalues. We study the eigenvalues of adjacency matrix of two types of star semigraphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-13T07:00:00Z
DOI: 10.1142/S1793830923500118
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- On the existence and construction of modular difference sets
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Authors: Osvaldo Marrero
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
The concept of a modular difference set was originally motivated by the cognate notion of modular Hadamard matrices, which have been researched extensively. We initiate the study of the repetition-parameter set in a modular difference set, and we relate the repetition-parameter set to integer partitions and Diophantine equations. By example, we show how a computational study of integer partitions can improve the upper bound on the size of such repetition-parameter set. All previously known examples of modular difference sets in a direct product of groups are concerned with a product of just two groups. We present new constructions of modular difference sets in a direct product of [math] groups. These new constructions suggest that the size of the repetition-parameter set is intimately related to the group’s structure. A generalization of difference sets, partial difference sets, and relative difference sets, modular difference sets have been used to construct both modular symmetric designs and equiangular tight frames in finite fields.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-13T07:00:00Z
DOI: 10.1142/S1793830923500180
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- On [math]-total edge irregular labelings
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Authors: Sarbari Mitra, Soumya Bhoumik
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A total edge irregular [math]-labeling of a graph [math], [math] is a labeling of vertices and edges of [math] in such a way that the weights of all edges are distinct. A total edge irregularity strength of graph [math], denoted by [math] is defined as the minimum [math] for which a graph [math] has a totally irregular total [math]-labeling. In this paper, we define [math]-total edge irregularity labeling and provide the irregularity strength for some well-known families of graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-03-09T08:00:00Z
DOI: 10.1142/S1793830923500106
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- Co-normal products and modular products of soft graphs
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Authors: Bobin George, Jinta Jose, Rajesh K. Thumbakara
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Most of our conventional tools for formal reasoning, computing, and modeling are precise, deterministic, and crisp. However, many complicated problems in the domains of economics, medicine, engineering, the environment, social science, and other disciplines demand data that is not always precise. We cannot always use traditional approaches because there are so many different types of uncertainty present in these problems. This difficulty could be caused by the parameterization tool’s insufficiency. Soft set theory, which Molodtsov presented in 1999, is a generic mathematical approach for handling uncertain data. Many researchers are currently using soft set theory to solve problems involving decision-making. The concept of soft graphs is used to provide a parameterized point of view for graphs. The topic of graph products has received a lot of interest in graph theory. It is a binary operation on graphs with numerous combinatorial uses. On soft graphs, we can define product operations in a manner similar to how graph products are defined. The co-normal product, the restricted co-normal product, the modular product, and the restricted modular product of soft graphs are all introduced in this study. We prove that these products of soft graphs are again soft graphs and derive methods for computing their vertex count, edge count, and the sum of part degrees.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-02-28T08:00:00Z
DOI: 10.1142/S179383092350012X
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- On the power graph of a monogenic semigroup
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Authors: Biswaranjan Khanra, Manasi Mandal, Buddha Dev Ghosh
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a monogenic semigroup with zero. Here, we consider the power graph [math] over [math] with vertex set [math] and two distinct vertices [math] and [math] are adjacent if [math] divides [math] or [math] divides [math], where [math]. We compute various graph parameters of [math] and topological indices based on distance of vertices. Finally, we compute some graph parameters of the cartesian product [math] of graphs [math] and [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-02-23T08:00:00Z
DOI: 10.1142/S1793830923500052
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- Strong 2-degenerate graph embeddings
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Authors: Peng Ying, Xia Zhang
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A result of Friedman and Pippenger gives a sufficient condition on the expansion properties of a graph to contain all small trees with bounded maximum degree. In this paper, we extend the tree embedding problem of expanding graphs to the degenerate graph embedding problem, and give a sufficient condition for a graph to contain strong [math]-degenerate subgraphs with bounded maximum codegree.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-02-02T08:00:00Z
DOI: 10.1142/S1793830923500076
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- A short note on hyperenergetic Cayley graphs
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Authors: Yushi Wu, Weijun Liu, Lu Lu
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A graph [math] on [math] vertices is called a hyperenergetic graph if [math] where [math] is the energy of [math]. In this paper, we consider hyperenergetic Cayley graphs. In detail, for any abelian group [math], we construct a class of Cayley graphs over [math], in which almost all are hyperenergetic. Furthermore, we also construct such a class of Cayley graphs over the dihedral group.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-01-31T08:00:00Z
DOI: 10.1142/S1793830923500027
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- “Riesel” and another numbers
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Authors: Krzysztof Kowitz, Karolina Miszczyk
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we will introduce “Riesel” numbers and we show closed formulae for calculating the [math]th “Riesel” number [math], the number of “Riesel” numbers up to [math], and the sum of the first [math] “Riesel” numbers. We will explore the relationships between the selected numbers and solve two special cases of diophantine equations.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-01-26T08:00:00Z
DOI: 10.1142/S1793830923300011
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- Maker-Breaker metric resolving games on graphs
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Authors: Cong X. Kang, Eunjeong Yi
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] denote the length of a shortest path between vertices [math] and [math] in a graph [math] with vertex set [math]. For a positive integer [math], let [math] and [math]. A set [math] is a distance-[math] resolving set of [math] if [math] for distinct [math]. In this paper, we study the maker-breaker distance-[math] resolving game (MB[math]RG) played on a graph [math] by two players, Maker and Breaker, who alternately select a vertex of [math] not yet chosen. Maker wins by selecting vertices which form a distance-[math] resolving set of [math], whereas Breaker wins by preventing Maker from winning. We denote by [math] the outcome of MB[math]RG. Let [math], [math] and [math], respectively, denote the outcome for which Maker, Breaker, and the first player has a winning strategy in MB[math]RG. Given a graph [math], the parameter [math] is a non-decreasing function of [math] with codomain [math]. We exhibit pairs [math] and [math] such that the ordered pair [math] realizes each member of the set [math]; we provide graphs [math] such that [math], [math] and [math] for [math]. Moreover, we obtain some general results on MB[math]RG and study the MB[math]RG played on some graph classes.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-01-25T08:00:00Z
DOI: 10.1142/S1793830923500064
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- On the ideal-based zero-divisor graph of commutative rings
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Authors: K. Selvakumar, N. Anusha
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a finite commutative ring with identity, [math] be an ideal of [math] and [math] denotes the Jacobson radical of [math]. The ideal-based zero-divisor graph [math] of [math] is a graph with vertex set [math] for some [math] in which distinct vertices [math] and [math] are adjacent if and only if [math]. In this paper, we determine the diameter, girth of [math]. Specifically, we classify all finite commutative nonlocal rings for which [math] is perfect. Furthermore, we discuss about the planarity, outerplanarity, genus and crosscap of [math] and characterize all of them.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-01-21T08:00:00Z
DOI: 10.1142/S1793830922501907
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- Semigroup structures via IVI-octahedron sets
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Authors: J. I. Baek, G. Muhiuddin, S. H. Han, K. Hur
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we use IVI-octahedron ideals and IVI-octahedron bi-ideals to discuss some characterizations of special semigroups, e.g., an intra-regular semigroup, a semigroup which is semilattice of left [respectively, right] simple semigroups or simple left groups and a semigroup which is a semilattice of groups and a [respectively, left and right] simple semigroups. Finally, we define an IVIO-simple [IVIOL-simple and IVI) R-simple] semigroup and study some of its properties and we give a characterization of a semisimple semigroup by IVIOIs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-01-21T08:00:00Z
DOI: 10.1142/S1793830923500015
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- Inverse fair domination in the join and corona of graphs
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Authors: Enrico L. Enriquez
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
Let [math] be a connected simple graph. A dominating subset [math] of [math] is a fair dominating set of [math] if all the vertices not in [math] are dominated by the same number of vertices from [math]. Let [math] be a minimum fair dominating set of [math]. A fair dominating set [math] is called an inverse fair dominating set of [math] with respect to [math]. The inverse fair domination number of [math] denoted by [math] is the minimum cardinality of an inverse fair dominating set of [math]. In this paper, we investigate the concept and give some important results. Further, we give the characterization of an inverse fair dominating set in the join and corona of two graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-01-19T08:00:00Z
DOI: 10.1142/S1793830923500039
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- On a generalization of Roman domination with more legions
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Authors: Fahimeh Khosh-Ahang Ghasr
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
In this paper, we generalize the concepts of (perfect) Roman and Italian dominations to (perfect) strong Roman and Roman [math]-domination for arbitrary positive integer [math]. These generalizations cover some of previous ones. After some comparison of their domination numbers, as a first study of these concepts, we study the (perfect, strong, perfect strong) Roman [math]-domination numbers of complete bipartite graphs.
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-01-19T08:00:00Z
DOI: 10.1142/S1793830923500040
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- Approximation algorithm for minimum [math]-dominator partization problem
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Authors: Sayani Das, Sounaka Mishra
Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print.
A dominator coloring of a graph [math] is a proper vertex coloring with a domination property that each vertex dominates a color class. The minimum number of colors used in a dominator coloring of [math] is called dominator chromatic number of [math] and is denoted as [math]. Graphs with [math] have characterizations and such graphs can be recognized in polynomial time. However, for [math], deciding whether [math] is [math]-hard. In this paper, we investigate the computational complexity of minimum [math]-dominator partization problem (Min-[math]-D-Partz). In Min-[math]-D-Partz, given a graph [math], the objective is to find a vertex set [math] of minimum size such that [math]. We prove that Min-[math]-D-Partz is [math]-complete and has a two-factor approximation algorithm. We also prove that Min-[math]-D-Partz cannot be approximated within any constant factor and can be approximated within a factor of [math].
Citation: Discrete Mathematics, Algorithms and Applications
PubDate: 2023-01-09T08:00:00Z
DOI: 10.1142/S1793830922501889
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