Authors:Nuttawoot Nupo, Sayan Panma Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. Let [math] denote the Cayley digraph of the rectangular group [math] with respect to the connection set [math] in which the rectangular group [math] is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. An independent dominating set of [math] is the independent set of elements in [math] that can dominate the whole elements. In this paper, we investigate the independent domination number of [math] and give more results on Cayley digraphs of left groups and right groups which are specific cases of rectangular groups. Moreover, some results of the path independent domination number of [math] are also shown. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:44:15Z DOI: 10.1142/S1793830918500246

Authors:Hong-Hai Li, Yi-Ping Liang Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. A matching of a graph [math] is a set of pairwise nonadjacent edges of [math], and a [math]-matching is a matching consisting of [math] edges. In this paper, we characterize the bicyclic graphs whose complements have the extremal number of [math]-matchings for all [math]. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:44:13Z DOI: 10.1142/S1793830918500167

Authors:Yuehua Bu, Chentao Qi Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. A [math]-injective edge coloring of a graph [math] is a coloring [math], such that if [math], [math] and [math] are consecutive edges in [math], then [math]. [math] has a [math]-injective edge coloring[math] is called the injective edge coloring number. In this paper, we consider the upper bound of [math] in terms of the maximum average degree mad[math], where [math]. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:44:08Z DOI: 10.1142/S1793830918500222

Authors:Ni̇hal Taş, Sümeyra Uçar, Ni̇hal Yilmaz Özgür, Öznur Öztunç Kaymak Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. In this paper, we present a new method of coding/decoding algorithms using Fibonacci [math]-matrices. This method is based on the blocked message matrices. The main advantage of our model is the encryption of each message matrix with different keys. Our approach will not only increase the security of information but also has high correct ability. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:44:04Z DOI: 10.1142/S1793830918500283

Authors:Yafang Hu, Weifan Wang Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. A [math]-distance vertex-distinguishing total coloring of a graph [math] is a proper total coloring of [math] such that any pair of vertices at distance [math] have distinct sets of colors. The [math]-distance vertex-distinguishing total chromatic number [math] of [math] is the minimum number of colors needed for a [math]-distance vertex-distinguishing total coloring of [math]. In this paper, we determine the [math]-distance vertex-distinguishing total chromatic number of some graphs such as paths, cycles, wheels, trees, unicycle graphs, [math], and [math]. We conjecture that every simple graph [math] with maximum degree [math] satisfies [math]. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:44:00Z DOI: 10.1142/S1793830918500180

Authors:J. Amjadi Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. Let [math] be a finite simple digraph with vertex set [math]. A signed total Roman dominating function (STRDF) on a digraph [math] is a function [math] such that (i) [math] for every [math], where [math] consists of all inner neighbors of [math], and (ii) every vertex [math] for which [math] has an inner neighbor [math] for which [math]. The weight of an STRDF [math] is [math]. The signed total Roman domination number [math] of [math] is the minimum weight of an STRDF on [math]. A set [math] of distinct STRDFs on [math] with the property that [math] for each [math] is called a signed total Roman dominating family (STRD family) (of functions) on [math]. The maximum number of functions in an STRD family on [math] is the signed total Roman domatic number of [math], denoted by [math]. In this paper, we initiate the study of signed total Roman domatic number in digraphs and we present some sharp bounds for [math]. In addition, we determine the signed total Roman domatic number of some classes of digraphs. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:56Z DOI: 10.1142/S1793830918500209

Authors:Mohammad M. Karbasioun, Gennady Shaikhet, Ioannis Lambadaris, Evangelos Kranakis Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. We study the problem of scheduling random energy demands within a fixed normalized time horizon. Each demand has to be serviced without interruption at a constant intensity, while its duration is bounded by a pair of malleability constraints. Such constraints are assumed to be characterized by an i.i.d random vector that follows a general distribution. At each time instance, the total power consumption is computed as the sum of the intensities of all demands being serviced at that moment. Our objective is to minimize both the maximum and the total convex cost of the power consumption of the grid. The problem is considered in the asymptotic regime. In this regime, the number of demands is assumed to be large, and their (random) energy requirements are inversely proportional to the number of demands. Such setting allows us to introduce a linear-time scheduling policy and shows its asymptotic optimality with respect to both cost criteria. We first study the optimization problem in the case where all demands are available a priori, i.e., before scheduling starts. Then we extend our approach for the case of demand scheduling in an arbitrary length time horizon, where the demands arrive randomly during this time interval. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:53Z DOI: 10.1142/S1793830918500258

Authors:Pengcheng Liu, Xiaohui Huang Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. In a (full) set multicover (SMC) problem, the goal is to select a subcollection of sets to fully cover all elements, where an element is fully covered if it belongs to at least a required number of sets of the selected subcollection. In a partial set multicover (PSMC) problem, it is sufficient to fully cover a required fraction of elements. In this paper, we present a greedy algorithm for PSMC, and analyze the ratio between the cost of the computed solution and the cost of an optimal solution to the corresponding (full) SMC problem. We shall call this ratio as a partial-versus-full ratio. The motivation for such an analysis is to show that PSMC is fairly economic even when it can only be calculated approximately. It turns out that the partial-versus-full ratio of our algorithm is at most [math], where [math] is the requirement of an element, and [math] is the fraction of elements required to be fully covered. An example is given showing that this ratio is tight up to a constant. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:50Z DOI: 10.1142/S179383091850026X

Authors:Jun Lan, Wensong Lin Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. Let [math] be a graph and [math] a non-negative integer. Suppose [math] is a mapping from the vertex set of [math] to [math]. If, for any vertex [math] of [math], the number of neighbors [math] of [math] with [math] is less than or equal to [math], then [math] is called a [math]-relaxed [math]-coloring of [math]. And [math] is said to be [math]-colorable. The [math]-relaxed chromatic number of [math], denote by [math], is defined as the minimum integer [math] such that [math] is [math]-colorable. Let [math] and [math] be two positive integers with [math]. Denote by [math] the path on [math] vertices and by [math] the [math]th power of [math]. This paper determines the [math]-relaxed chromatic number of [math] the [math]th power of [math]. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:46Z DOI: 10.1142/S1793830918500179

Authors:Xiaofang Jiang, Qinghui Liu, N. Parthiban, R. Sundara Rajan Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. A linear arrangement is a labeling or a numbering or a linear ordering of the vertices of a graph. In this paper, we solve the minimum linear arrangement problem for bijective connection graphs (for short BC graphs) which include hypercubes, Möbius cubes, crossed cubes, twisted cubes, locally twisted cube, spined cube, [math]-cubes, etc., as the subfamilies. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:42Z DOI: 10.1142/S1793830918500234

Authors:Sohaib Khalid, Akbar Ali Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. The zeroth-order general Randić index (usually denoted by [math]) and variable sum exdeg index (denoted by [math]) of a graph [math] are defined as [math] and [math], respectively, where [math] is degree of the vertex [math], [math] is a positive real number different from 1 and [math] is a real number other than [math] and [math]. A segment of a tree is a path [math], whose terminal vertices are branching or/and pendent, and all non-terminal vertices (if exist) of [math] have degree 2. For [math], let [math], [math], [math] be the collections of all [math]-vertex trees having [math] pendent vertices, [math] segments, [math] branching vertices, respectively. In this paper, all the trees with extremum (maximum and minimum) zeroth-order general Randić index and variable sum exdeg index are determined from the collections [math], [math], [math]. The obtained extremal trees for the collection [math] are also extremal trees for the collection of all [math]-vertex trees having fixed number of vertices with degree 2 (because the number of segments of a tree [math] can be determined from the number of vertices of [math] having degree 2 and vice versa). Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:36Z DOI: 10.1142/S1793830918500155

Authors:Zemin Jin, Kun Ye, He Chen, Yuefang Sun Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. The lower bounds for the size of maximum rainbow matching in properly edge-colored graphs have been studied deeply during the last decades. An edge-coloring of a graph [math] is called a strong edge-coloring if each path of length at most three is rainbow. Clearly, the strong edge-coloring is a natural generalization of the proper one. Recently, Babu et al. considered the problem in the strongly edge-colored graphs. In this paper, we introduce a semi-strong edge-coloring of graphs and consider the existence of large rainbow matchings in it. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:30Z DOI: 10.1142/S1793830918500210

Authors:Zhihao Chen, Zhao Zhang Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. With the advent of big data era, it is more and more acceptable that the topology of a network can reveal more than we can conceive. In this paper, we propose an algorithm to predict a winner of an election among several competitors based on the relationships of individuals in a social network. Convergence is proved and an extensive experiment is done to show the effectiveness of the algorithm. Our algorithm can also be used to identify members of different parties in a fairly reasonable manner. Furthermore, our algorithm is merely based on the topology of the network, which saves us a large amount of work from collecting voting intentions and executing data pre-processing. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:24Z DOI: 10.1142/S1793830918500271

Authors:Ali Zeydi Abdian, S. Morteza Mirafzal Abstract: Discrete Mathematics, Algorithms and Applications, Volume 10, Issue 02, April 2018. In the past decades, graphs that are determined by their spectrum have received much more and more attention, since they have been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. An important part of spectral graph theory is devoted to determining whether given graphs or classes of graphs are determined by their spectra or not. So, finding and introducing any class of graphs which are determined by their spectra can be an interesting and important problem. The main aim of this study is to characterize two classes of multicone graphs which are determined by their adjacency, Laplacian and signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let [math] denote a complete graph on [math] vertices. In the paper, we show that multicone graphs [math] and [math] are determined by both their adjacency spectra and their Laplacian spectra, where [math] and [math] denote the Local Higman–Sims graph and the Local [math] graph, respectively. In addition, we prove that these multicone graphs are determined by their signless Laplacian spectra. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T06:43:16Z DOI: 10.1142/S1793830918500192

Authors:Ismail Aydogdu, Taher Abualrub Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. [math]-additive codes for any integer [math] are considered as codes over mixed alphabets. They are a generalization of binary linear codes and linear codes over [math] In this paper, we are interested in studying [math]-additive cyclic codes. We will give the generator polynomials of these codes. We will also give the minimal spanning sets for these codes. We will define separable [math]-additive codes and provide conditions on the generator polynomials for a [math]-additive cyclic code to be separable. Finally, we present some examples of optimal parameter binary codes obtained as images of [math]-additive cyclic codes. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-24T08:24:19Z DOI: 10.1142/S1793830918500489

Authors:Juan Li, Jian Gao, Yongkang Wang Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. In this paper, structural properties of [math]-constacyclic codes over the finite non-chain ring [math] are studied, where [math], [math], [math] and [math] is a power of some odd prime. As an application, some better quantum codes, compared with previous work, are obtained. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-23T08:30:03Z DOI: 10.1142/S1793830918500465

Authors:V. Aghapouramin, M. J. Nikmehr Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Let [math] be a commutative ring with identity which is not an integral domain. An ideal [math] of a ring [math] is called an annihilating ideal if there exists [math] such that [math]. Let [math] be a simple undirect graph associated with [math] whose vertex set is the set of all nonzero annihilating ideals of [math] and two distinct vertices [math] are joined if and only if [math] is also an annihilating ideal of [math]. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. In this paper, we characterize all rings whose [math] is perfect. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-23T08:30:02Z DOI: 10.1142/S1793830918500477

Authors:Hongping Ma, Xiaoxue Hu, Jiangxu Kong, Murong Xu Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. An [math]-hued coloring is a proper coloring such that the number of colors used by the neighbors of [math] is at least [math]. A linear [math]-hued coloring is an [math]-hued coloring such that each pair of color classes induces a union of disjoint paths. We study the linear list [math]-hued chromatic number, denoted by [math], of sparse graphs. It is clear that any graph [math] with maximum degree [math] satisfies [math]. Let [math] be the maximum average degree of a graph [math]. In this paper, we obtain the following results: [math] [math]. [math]. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-06T09:40:44Z DOI: 10.1142/S1793830918500453

Authors:Tao Pan, Lei Sun Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. It was proved in [Y. Bu and C. Shang, List 2-distance coloring of planar graphs without short cycles, Discrete Math. Algorithm. Appl. 8 (2016) 1650013] that for every planar graph with girth [math] and maximum degree [math] is list 2-distance [math]-colorable. In this paper, we proved that: for every planar graph with [math] and [math] is list 2-distance [math]-colorable. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-04-03T09:22:23Z DOI: 10.1142/S1793830918500441

Authors:Marina Moscarini, Francesco M. Malvestuto Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Monophonic, geodesic and 2-geodesic convexities ([math]-convexity, [math]-convexity and [math]-convexity, for short) on graphs are based on the families of induced paths, shortest paths and shortest paths of length [math], respectively. We introduce a class of graphs, the class of cross-cyclicgraphs, in which every connected [math]-convex set is also [math]-convex and [math]-convex. We show that this class is properly contained in the class, say [math], of graphs in which geodesic and monophonic convexities are equivalent and properly contains the class of distance-hereditary graphs. Moreover, we show that (1) an [math]-hull set (i.e., a subset of vertices, with minimum cardinality, whose [math]-convex hull equals the whole vertex set) and, hence, the m-hull number and the g-hull number of a graph in [math] can be computed in polynomial time and that (2) both the geodesic-convex hull and the monophonic-convex hull can be computed in linear time in a cross-cyclic graph without cycles of length [math] and, hence, in a bipartite distance-hereditary graph. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-28T06:55:47Z DOI: 10.1142/S1793830918500428

Authors:Terry A. McKee Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. The [math]-chordal graphs, defined by no induced cycle having length greater than [math], generalize the traditional chordal graphs (where [math]), which Dirac characterized in 1961 by minimal separators always inducing complete subgraphs. The more recent unichord-free graphs, defined by no cycle having a unique chord, have been characterized by minimal separators always inducing edgeless subgraphs. This sharp contrast of minimal separators motivates a new concept of [math]-unichord-free graphs, strengthening the unichord-free graphs (where [math]). The class of all unichord-free graphs decomposes into subclasses that are simultaneously [math]-chordal and [math]-unichord-free, leading to characterizations of some of these subclasses and to open questions about their overall structure as [math] and [math] increase. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-28T06:55:47Z DOI: 10.1142/S179383091850043X

Authors:Fang Wang, Xiaoping Liu Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Let [math] be a graph and [math] be a positive integer. The [math]-subdivision [math] of [math] is the graph obtained from [math] by replacing each edge by a path of length [math]. The [math]-power [math] of [math] is the graph with vertex set [math] in which two vertices [math] and [math] are adjacent if and only if the distance [math] between [math] and [math] in [math] is at most [math]. Note that [math] is the total graph [math] of [math]. The chromatic number [math] of [math] is the minimum integer [math] for which [math] has a proper [math]-coloring. The total chromatic number of [math], denoted by [math], is the chromatic number of [math]. Rosenfeld [On the total coloring of certain graphs, Israel J. Math. 9 (1971) 396–402] and independently, Vijayaditya [On total chromatic number of a graph, J. London Math. Soc. 2 (1971) 405–408] showed that for a subcubic graph [math], [math]. In this note, we prove that for a subcubic graph [math], [math]. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-19T08:42:57Z DOI: 10.1142/S1793830918500416

Authors:Sudev Naduvath Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Coloring the vertices of a graph [math] subject to given conditions can be considered as a random experiment and corresponding to this experiment, a discrete random variable [math] can be defined as the color of a vertex chosen at random, with respect to the given type of coloring of [math] and a probability mass function for this random variable can be defined accordingly. A proper coloring [math] of a graph [math], which assigns colors to the vertices of [math] such that the numbers of vertices in any two color classes differ by at most one, is called an equitable coloring of [math]. In this paper, we study two statistical parameters of certain graphs, with respect to their equitable colorings. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-19T08:42:56Z DOI: 10.1142/S1793830918500404

Authors:F. Heydari Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Let [math] be a commutative ring and [math] be an [math]-module, and let [math] be the set of all nontrivial ideals of [math]. The [math]-intersection graph of ideals of [math], denoted by [math], is a graph with the vertex set [math], and two distinct vertices [math] and [math] are adjacent if and only if [math]. For every multiplication [math]-module [math], the diameter and the girth of [math] are determined. Among other results, we prove that if [math] is a faithful [math]-module and the clique number of [math] is finite, then [math] is a semilocal ring. We denote the [math]-intersection graph of ideals of the ring [math] by [math], where [math] are integers and [math] is a [math]-module. We determine the values of [math] and [math] for which [math] is perfect. Furthermore, we derive a sufficient condition for [math] to be weakly perfect. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-19T08:42:55Z DOI: 10.1142/S1793830918500386

Authors:Yulong Wei, Min Xu, Kaishun Wang Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. In 2011, Li et al. [The (strong) rainbow connection numbers of Cayley graphs on Abelian groups, Comput. Math. Appl. 62(11) (2011) 4082–4088] obtained an upper bound of the strong rainbow connection number of an [math]-dimensional undirected toroidal mesh. In this paper, this bound is improved. As a result, we give a negative answer to their problem. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-19T08:42:50Z DOI: 10.1142/S1793830918500398

Authors:Anwar Alwardi, Akram Alqesmah, R. Rangarajan, Ismail Naci Cangul Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. The Zagreb indices have been introduced in 1972 to explain some properties of chemical compounds at molecular level mathematically. Since then, the Zagreb indices have been studied extensively due to their ease of calculation and their numerous applications in place of the existing chemical methods which needed more time and increased the costs. Many new kinds of Zagreb indices are recently introduced for several similar reasons. In this paper, we introduce the entire Zagreb indices by adding incidency of edges and vertices to the adjacency of the vertices. Our motivation in doing so was the following fact about molecular graphs: The intermolecular forces do not only exist between the atoms, but also between the atoms and bonds, so one should also take into account the relations (forces) between edges and vertices in addition to the relations between vertices to obtain better approximations to intermolecular forces. Exact values of these indices for some families of graphs are obtained and some important properties of the entire Zagreb indices are established. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-19T08:42:48Z DOI: 10.1142/S1793830918500374

Authors:Anuradha Sharma, Tania Sidana Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Let [math] be a prime, [math] be a positive integer, and let GR[math] be the Galois ring of characteristic [math] and cardinality [math]. In this paper, all repeated-root constacyclic codes of arbitrary lengths over GR[math] their sizes and their dual codes are determined. As an application, some isodual constacyclic codes over GR[math] are also listed. To illustrate the results, all cyclic and negacyclic codes of length 10 over GR(4,3) are obtained. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-08T02:55:05Z DOI: 10.1142/S1793830918500362

Authors:Amit Sharma, Ramakrishna Bandi, Maheshanand Bhaintwal Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. In this paper, we study cyclic codes over [math]. A necessary and sufficient condition for a cyclic code over [math] to contain its dual is determined. The odd and even length cases are discussed separately to obtain above condition. It is shown that Gray image of a cyclic code over [math] containing its dual is a linear code over [math] which also contains its dual. We have then obtained the parameters of corresponding CSS-quantum codes over [math]. By augmentation, we construct codes with dual-containing property from codes of smaller size containing their duals. Through this construction, we have obtained some optimal quantum codes over [math]. Some examples have been given to illustrate the results. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-02T07:56:36Z DOI: 10.1142/S1793830918500337

Authors:Monireh Jahani Sayyad Noveiri, Sohrab Kordrostami, Alireza Amirteimoori Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Data envelopment analysis (DEA) is a technique to evaluate the relative efficiency of a set of decision making units (DMUs) which is applicable in different systems such as engineering, ecology, and so forth. In real-world situations, there are instances in which production processes of systems must be analyzed in multiple periods while desirable and undesirable outputs are present; therefore, in the current paper, a DEA-based procedure is suggested to estimate the performance of systems with desirable and undesirable outputs over several periods of time. Actually, the overall and period efficiencies of DMUs in the presence of undesirable outputs are calculated by using the DEA technique. Different aspects of disposability, i.e., strong and weak, are considered for undesirable outputs. Moreover, the overall efficiency is indicated as a weighted average of the efficiencies of periods. Efficiency changes between two periods are also estimated. The proposed approach has been tested by a numerical example and applied to evaluate the efficiency of commercial transport industry in 17 countries. The findings show that efficiency scores and their changes between periods might alter by incorporating undesirable outputs into the multi-period system under evaluation; consequently, the proposed approach obtains more rational and accurate results when undesirable outputs are present. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-02T07:56:36Z DOI: 10.1142/S1793830918500349

Authors:Abdollah Alhevaz, Maryam Baghipur, Somnath Paul Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. The distance signless Laplacian spectral radius of a connected graph [math] is the largest eigenvalue of the distance signless Laplacian matrix of [math], defined as [math], where [math] is the distance matrix of [math] and [math] is the diagonal matrix of vertex transmissions of [math]. In this paper, we determine some bounds on the distance signless Laplacian spectral radius of [math] based on some graph invariants, and characterize the extremal graphs. In addition, we define distance signless Laplacian energy, similar to that in [J. Yang, L. You and I. Gutman, Bounds on the distance Laplacian energy of graphs, Kragujevac J. Math. 37 (2013) 245–255] and give some bounds on the distance signless Laplacian energy of graphs. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-03-02T07:56:35Z DOI: 10.1142/S1793830918500350

Authors:Arti Sharma, Atul Gaur Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Let [math] be a commutative ring with nonzero identity. Let [math] denote the maximal graph associated to [math], that is, [math] is a graph with vertices as non-units of [math], where two distinct vertices [math] and [math] are adjacent if and only if there is a maximal ideal of [math] containing both. In this paper, we characterize the finite commutative rings such that their maximal graph are planar graphs, and we also study the case where they are outerplanar and ring graphs. The equivalence of outerplanar graphs and ring graphs for [math] is established. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-02-26T09:24:09Z DOI: 10.1142/S1793830918500325

Authors:N. K. Sudev, K. P. Chithra, K. A. Germina, S. Satheesh, Johan Kok Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Coloring the vertices of a graph [math] according to certain conditions can be considered as a random experiment and a discrete random variable [math] can be defined as the number of vertices having a particular color in the proper coloring of [math]. The concepts of mean and variance, two important statistical measures, have also been introduced to the theory of graph coloring and determined the values of these parameters for a number of standard graphs. In this paper, we discuss the coloring parameters of the Mycielskian of certain standard graphs. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-02-22T09:01:51Z DOI: 10.1142/S1793830918500301

Authors:Supawadee Prugsapitak, Somphong Jitman Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Self-dual cyclic codes form an important class of linear codes. It has been shown that there exists a self-dual cyclic code of length [math] over a finite field if and only if [math] and the field characteristic are even. The enumeration of such codes has been given under both the Euclidean and Hermitian products. However, in each case, the formula for self-dual cyclic codes of length [math] over a finite field contains a characteristic function which is not easily computed. In this paper, we focus on more efficient ways to enumerate self-dual cyclic codes of lengths [math] and [math], where [math], [math], and [math] are positive integers. Some number theoretical tools are established. Based on these results, alternative formulas and efficient algorithms to determine the number of self-dual cyclic codes of such lengths are provided. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-02-22T09:01:51Z DOI: 10.1142/S1793830918500313

Authors:Ali Jafari Taloukolaei, Shervin Sahebi Abstract: Discrete Mathematics, Algorithms and Applications, Ahead of Print. Let [math] be a ring with nonzero identity. By the Von Neumann regular graph of [math], we mean the graph that its vertices are all elements of [math] such that there is an edge between vertices [math] if and only if [math] is a Von Neumann regular element of [math], denoted by [math]. In this paper, the basic properties of [math] are investigated and some characterization results regarding connectedness, diameter, girth and planarity of [math] are given. Citation: Discrete Mathematics, Algorithms and Applications PubDate: 2018-02-22T09:01:50Z DOI: 10.1142/S1793830918500295