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  Subjects -> MATHEMATICS (Total: 955 journals)
    - APPLIED MATHEMATICS (82 journals)
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    - MATHEMATICS (706 journals)
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MATHEMATICS (706 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 27)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 6)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 3)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 5)
Advances in Science and Research (ASR)     Open Access   (Followers: 4)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 10)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Electronic Notes in Discrete Mathematics
  [SJR: 0.32]   [H-I: 15]   [2 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 1571-0653
   Published by Elsevier Homepage  [3175 journals]
  • Some results on the Laplacian spectra of graphs with pockets
    • Authors: Sasmita Barik; Gopinath Sahoo
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Sasmita Barik, Gopinath Sahoo
      Let F, H v be simple connected graphs on n and m+1 vertices, respectively. Let v be a specified vertex of H v and u 1 , … , u k ∈ F . Then the graph G = G [ F , u 1 , … , u k , H v ] obtained by taking one copy of F and k copies of H v , and then attaching the i-th copy of H v to the vertex u i , i = 1 , … , k , at the vertex v of H v (identify u i with the vertex v of the i-th copy) is called a graph with k pockets. In [Barik, S., On the Laplacian spectra of graphs with pockets, Linear and Multilinear Algebra, 56 (2008), 481–490], Barik raised the question that ‘how far can the Laplacian spectrum of G be described by using the Laplacian spectra of F and H v '’ and discussed the case when deg(v) = m in H v . In this article, we study the problem for more general cases and describe the Laplacian spectrum. As an application, we construct new nonisomorphic Laplacian cospectral graphs from the known ones.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.akcej.2017.11.004
      Issue No: Vol. 63 (2017)
       
  • Forbidden Induced Subgraphs
    • Authors: Thomas Zaslavsky
      Pages: 3 - 10
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Thomas Zaslavsky
      In descending generality I survey: five partial orderings of graphs, the induced-subgraph ordering, and examples like perfect, threshold, and mock threshold graphs. The emphasis is on how the induced subgraph ordering differs from other popular orderings and leads to different basic questions.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.10.056
      Issue No: Vol. 63 (2017)
       
  • C-Cordial Labeling in Signed Graphs
    • Authors: Mukti Acharya
      Pages: 11 - 22
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Mukti Acharya
      In this paper, we initiate the study on C-cordial labeling in signed graphs and characterize paths and cycles with given number of negative sections and stars which admit C-cordial labeling.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.10.057
      Issue No: Vol. 63 (2017)
       
  • Open Problems for Hanoi and Sierpiński Graphs
    • Authors: Andreas M. Hinz
      Pages: 23 - 31
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Andreas M. Hinz
      We list some unsolved problems concerning two meanwhile famous classes of graphs, namely the Hanoi graphs and the Sierpiński graphs. Whereas many graph parameters have been determined and metric properties are well-understood for the latter, the former give rise to notoriously difficult questions, in particular when it comes to distance-related tasks.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.10.058
      Issue No: Vol. 63 (2017)
       
  • On Edge-Graceful Regular Graphs with Particular 3-Factors
    • Authors: Tao-Ming Wang; Guang-Hui Zhang
      Pages: 33 - 40
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Tao-Ming Wang, Guang-Hui Zhang
      An edge-graceful labeling of a finite simple graph with p vertices and q edges is a bijection from the set of edges to the set of integers { 1 , 2 , ⋯ , q } such that the vertex sums are pairwise distinct modulo p, where the vertex sum at a vertex is the sum of labels of all edges incident to such vertex. A graph is called edge-graceful if it admits an edge-graceful labeling. In this article, we verify that an regular graph of odd degree is edge-graceful if it contains either of two particular 3-regular spanning subgraphs, namely, a quasi-prism factor and a claw factor.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.10.059
      Issue No: Vol. 63 (2017)
       
  • Negative Circles in Signed Graphs: A Problem Collection
    • Authors: Thomas Zaslavsky
      Pages: 41 - 47
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Thomas Zaslavsky
      I propose that most problems about circles (cycles, circuits) in ordinary graphs that have odd or even length find their proper setting in the theory of signed graphs, where each edge has a sign, + or −. Even-circle and odd-circle problems correspond to questions about positive and negative circles in signed graphs. (The sign of a circle is the product of its edge signs.) I outline questions about circles in signed graphs, that seem natural and potentially important.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.10.060
      Issue No: Vol. 63 (2017)
       
  • Bounds for the sum choice number
    • Authors: Arnfried Kemnitz; Massimiliano Marangio; Margit Voigt
      Pages: 49 - 58
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Arnfried Kemnitz, Massimiliano Marangio, Margit Voigt
      A simple graph G = ( V , E ) is called L-colorable if there is a proper coloring c of the vertices with c ( v ) ∈ L ( v ) for all v ∈ V where L ( v ) is an assignment of colors to v. A function f : V → N is called a choice function of G if G is L-colorable for every assignment L with L ( v ) = f ( v ) for all v ∈ V . The sum choice number χ s c ( G ) of G is defined as the minimum of ∑ v ∈ V f ( v ) over all choice functions f of G. In this note we give general lower and upper bounds for the sum choice number. We determine all connected graphs G whose sum choice number attains the lower bound 2 V − 1 or 2 V . Moreover, we determine all complete multipartite graphs whose sum choice number attains the upper bound V + E .

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.10.061
      Issue No: Vol. 63 (2017)
       
  • Genus of total graphs of commutative rings: A survey
    • Authors: T. Asir; T. Tamizh Chelvam
      Pages: 59 - 68
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): T. Asir, T. Tamizh Chelvam
      The topological properties of graphs are well studied. More specifically the genus of graphs and their embeddings are attractions to many authors. In this survey, we present the results concerning the genus of total graph and generalized the total graph and generalized total graphs of commutative rings.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.10.062
      Issue No: Vol. 63 (2017)
       
  • Reduced power graph of a group
    • Authors: R. Rajkumar; T. Anitha
      Pages: 69 - 76
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): R. Rajkumar, T. Anitha
      Let S be a semigroup. We define the directed reduced power graph of S, denoted by P → ( S ) , is a digraph with vertex set S, and for u, v ∈ S, there is an arc from u to v if and only if u ≠ v and 〈 v 〉 ⊂ 〈 u 〉 . The (undirected) reduced power graph of S, denoted by P ( S ) , is the underlying graph of P → ( S ) . This means that the set of vertices of P ( S ) is equal to S and two vertices u and v are adjacent if and only if u ≠ v and 〈 v 〉 ⊂ 〈 u 〉 or 〈 u 〉 ⊂ 〈 v 〉 . In this paper, we study some interplay between the algebraic properties of a group and the graph theoretic properties of its (directed and undirected) reduced power graphs. Also we establish some relationship between the reduced power graphs and power graphs of groups.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.10.063
      Issue No: Vol. 63 (2017)
       
  • Complexity Issues of Variants of Secure Domination in Graphs
    • Authors: Devendra Lad; P. Venkata Subba Reddy; J. Pavan Kumar
      Pages: 77 - 84
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Devendra Lad, P. Venkata Subba Reddy, J. Pavan Kumar
      Let G = ( V , E ) be a simple, undirected and connected graph. A connected dominating set S ⊆ V ( G ) is a secure connected dominating set of G, if for each u ∈ V ( G ) \ S , there exists v ∈ S such that ( u , v ) ∈ E ( G ) and the set ( S \ { v } ) ∪ { u } is a connected dominating set of G. The minimum cardinality of a secure connected dominating set of G denoted γ s c ( G ) , is called the secure connected domination number of G. In this paper, we show that the decision problems of finding a minimum secure connected dominating set and a minimum secure total dominating set are NP-complete for split graphs. We initiate the study of 2-secure domination and show that the decision problem corresponding to the computation of 2-secure domination number of a graph is NP-complete, even when restricted to split graphs or bipartite graphs. Finally we show that given two positive integers k ( ≥ 2 ) and n ( ≥ max ⁡ { 4 , k } ) there exists a graph G with V ( G ) = n and γ s c ( G ) = k .

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.001
      Issue No: Vol. 63 (2017)
       
  • Further results on the radio number of trees
    • Authors: Devsi Bantva
      Pages: 85 - 91
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Devsi Bantva
      Let G be a finite, connected, undirected graph with diameter diam(G) and d(u, v) denote the distance between u and v in G. A radio labeling of a graph G is a mapping f : V ( G ) → { 0 , 1 , 2 , … } such that f ( u ) − f ( v ) ≥ diam ( G ) + 1 − d ( u , v ) for every pair of distinct vertices u, v of G. The radio number of G, denoted by rn(G), is the smallest integer k such that G has a radio labeling f with max ⁡ { f ( v ) : v ∈ V ( G ) } = k . In this paper, we determine the radio number for three families of trees obtained by taking graph operation on a given tree or a family of trees.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.002
      Issue No: Vol. 63 (2017)
       
  • Radio number for middle graph of paths
    • Authors: Devsi Bantva
      Pages: 93 - 100
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Devsi Bantva
      For a connected graph G, let diam(G) and d(u, v) denote the diameter of G and distance between u and v in G. A radio labeling of a graph G is a mapping ϕ : V ( G ) → { 0 , 1 , 2 , … } such that ϕ ( u ) − ϕ ( v ) ≥ diam ( G ) + 1 − d ( u , v ) for every pair of distinct vertices u, v of G. The span of ϕ is defined as span ( ϕ ) = max ⁡ { ϕ ( u ) − ϕ ( v ) : u , v ∈ V ( G ) } . The radio number rn(G) of G is defined as rn ( G ) = min ⁡ { span ( ϕ ) : ϕ  is a radio labeling of  G } . In this paper, we determine the radio number for middle graph of paths.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.003
      Issue No: Vol. 63 (2017)
       
  • New Terminology and Results for AVL Trees
    • Authors: Mahdi Amani
      Pages: 101 - 108
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Mahdi Amani
      We introduce gaps which are special edges or external pointers in AVL trees such that the height difference between the subtrees rooted at two endpoints of a gap is equal to 2. Using gaps we prove the Basic-Theorem which illustrates how the size of an AVL tree (and its subtrees) can be represented by a series of powers of 2 of the heights of the gaps, this theorem is the first such a simple formula to characterize the number of nodes in an AVL tree. Then, we study the extreme case of AVL trees, the perfectly unbalanced AVL trees, by defining Fibonacci-isomorphic trees, and we show that they have the maximum number of gaps in AVL trees. In the rest of the paper, we study combinatorial properties of these trees. Keywords: AVL tree, Fibonacci tree, Fibonacci-isomorphic tree, Gaps in AVL tree, Subtree size, Enumeration, Encoding.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.004
      Issue No: Vol. 63 (2017)
       
  • Estimation of Expressions' Complexities for Two-Terminal Directed Acyclic
           Graphs
    • Authors: Mark Korenblit; Vadim E. Levit
      Pages: 109 - 116
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Mark Korenblit, Vadim E. Levit
      The paper investigates relationship between algebraic expressions and graphs. Our intention is to simplify graph expressions and eventually find their shortest representations. We prove the decomposition lemma which asserts that the shortest expression of a subgraph of a graph G is not larger than the shortest expression of G. Using this finding, we estimate an upper bound of a size of the shortest expression for any two-terminal directed acyclic graph.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.005
      Issue No: Vol. 63 (2017)
       
  • Location of Multiple Sub-Blocks with Burst Errors
    • Authors: Pankaj Kumar Das
      Pages: 117 - 123
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Pankaj Kumar Das
      Error locating code is a concept that compromise between short and long code length and identifies the corrupted sub-block(s) containing the error occurring within subblock(s). This paper presents bounds on the number of parity check digits of such error-locating codes that are capable of not only detecting any burst error of length b or less within a sub-block, but also can locate several such corrupted sub-blocks. We also provide an example of such a code.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.006
      Issue No: Vol. 63 (2017)
       
  • Utilization of OpenCL for Large Graph Problems on Graphics Processing Unit
    • Authors: Vinod Kumar Mishra; Pankaj Singh Sammal
      Pages: 125 - 135
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Vinod Kumar Mishra, Pankaj Singh Sammal
      During recent years graphics processing unit (GPU) has become an inexpensive high-performance parallel computing units and general purpose computation on graphics processing unit (GPGPU) become an alternative of conventional CPU computation, which provide massive parallel computation capability to a normal computer over a system which uses only CPU. This paper investigates the performance of the algorithm for the solution of single source shortest path (SSSP) problem, all pair shortest path (APSP) problem and graph coloring problem for large graph on GPU regardless of a specific vendor. The application programming interface (API) used for programming in graphic processing unit is open compute language (OpenCL), it is a specification for heterogeneous computing. The performance of solutions on GPU is compared with the solution on CPU in term of their execution time. The result indicates the significant improvement in the performance of the solutions on GPU over solutions on CPU.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.007
      Issue No: Vol. 63 (2017)
       
  • On Sum of Powers of the Laplacian Eigenvalues of Power Graphs of Certain
           Finite Groups
    • Authors: Sriparna Chattopadhyay; Pratima Panigrahi
      Pages: 137 - 143
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Sriparna Chattopadhyay, Pratima Panigrahi
      The power graph G ( G ) of a finite group G is the graph whose vertices are the elements of G and two distinct vertices are adjacent if and only if one is an integral power of the other. Here we concentrate on sum of powers of the non-zero Laplacian eigenvalues of G ( Z n ) and G ( D n ) . As a result we obtain bounds for Laplacian-energy-like (LEL) invariant of the same graphs.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.008
      Issue No: Vol. 63 (2017)
       
  • Degree and Distance Based Topological Indices of Graphs
    • Authors: K. Pattabiraman
      Pages: 145 - 159
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): K. Pattabiraman
      In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of Mycielskian graph and its complement are obtained. Also, we obtain the sharp upper and lower bounds for the sum- connectivity index of Mycielskian graph. (http://www.elsevier.com/locate/endm)

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.009
      Issue No: Vol. 63 (2017)
       
  • Degree exponent polynomial of graphs obtained by some graph operations
    • Authors: H.S. Ramane; S.S. Shinde
      Pages: 161 - 168
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): H.S. Ramane, S.S. Shinde
      The degree exponent matrix DE(G) of a graph G is a square matrix whose (i, j)-th entry is d i d j whenever i ≠ j , otherwise it is zero, where d i vertex of G. In this paper we obtain the characteristic polynomial of the degree exponent matrix of graphs obtained by some graph operations.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.010
      Issue No: Vol. 63 (2017)
       
  • On Enumeration of Some Non-isomorphic Edge Complete Semigraphs
    • Authors: Prabhakar R. Hampiholi; Jotiba P. Kitturkar
      Pages: 169 - 176
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Prabhakar R. Hampiholi, Jotiba P. Kitturkar
      Semigraph is introduced by E. Sampathkumar as a generalization of a graph. Semigraph G is edge complete if any two edges of G are adjacent. In this paper, we prove the special results on the enumeration of various categories of non-isomorphic edge complete semigraphs.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.011
      Issue No: Vol. 63 (2017)
       
  • A characterization of biconnected graphs reachable by robots jumping over
           m obstacles
    • Authors: Biswajit Deb
      Pages: 177 - 187
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Biswajit Deb
      Given two vertices u, v in a graph G, by C v u we denote the configuration of G with a robot at vertex u, a hole at vertex v and obstacles at the remaining vertices of G graph G is said to be complete S-reachable if starting from each configurations in G the robot can be taken to any other vertex of G by a sequence of moves consisting of simple moves of the obstacles and mRJ moves of the robot for m ∈ S , where S is a finite non-empty set of non-negative integers. An mRJ move on C v u is the process of moving the robot from u to v by jumping over m obstacles if there is a u-v path of length m + 1 in G. A 0 R J move is known as a simple move. We characterize the biconnected graphs that are complete { m } -reachable, for some positive integer m.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.012
      Issue No: Vol. 63 (2017)
       
  • Graceful labeling of some zero divisor graphs
    • Authors: Sarifa Khatun; Sk. Md. Abu Nayeem
      Pages: 189 - 196
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Sarifa Khatun, Sk. Md. Abu Nayeem
      This paper contains some results on graceful labeling of some zero divisor graphs. We prove that the zero divisor graph of Z n , the commutative ring of integers modulo n, is graceful if n = pq or 4p or 9p, where p and q both are prime numbers.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.013
      Issue No: Vol. 63 (2017)
       
  • On the power graph of the direct product of two groups
    • Authors: A.K. Bhuniya; Sajal Kumar Mukherjee
      Pages: 197 - 202
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): A.K. Bhuniya, Sajal Kumar Mukherjee
      The power graph P (G) of a finite group G is the graph with vertex set G and two distinct vertices are adjacent if either of them is a power of the other. Here we show that the power graph P ( G 1 × G 2 ) of the direct product of two groups G 1 and G 2 is not isomorphic to either of the direct, cartesian and normal product of their power graphs P (G 1) and P (G 2). A new product of graphs, namely generalized product, has been introduced and we prove that the power graph P ( G 1 × G 2 ) is isomorphic to a generalized product of P (G 1) and P (G 2).

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.014
      Issue No: Vol. 63 (2017)
       
  • Restrained Domination in Some Subclasses of Chordal Graphs
    • Authors: Arti Pandey; B.S. Panda
      Pages: 203 - 210
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Arti Pandey, B.S. Panda
      A set D ⊆ V of a graph G = (V, E) is called a restrained dominating set of G if every vertex not in D is adjacent to a vertex in D and to a vertex in V \ D . The Minimum Restrained Domination problem is to find a restrained dominating set of minimum cardinality. The decision version of the Minimum Restrained Domination problem is known to be NP-complete for chordal graphs. In this paper, we strengthen this NP-completeness result by showing that the problem remains NP-complete for doubly chordal graphs, a subclass of chordal graphs. We also propose a polynomial time algorithm to solve the Minimum Restrained Domination problem in block graphs, a subclass of doubly chordal graphs.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.015
      Issue No: Vol. 63 (2017)
       
  • Edge irredundant colorings in graphs
    • Authors: K. Raja Chandrasekar; A. Mohammed Abid
      Pages: 211 - 218
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): K. Raja Chandrasekar, A. Mohammed Abid
      An edge irredundant coloring of a graph G = (V, E) is an edge partition ∏ = { E 1 , E 2 , … , E k } of E into nonempty edge irredundant sets. The edge irratic number is the minimum order of an edge irredundant coloring of G and it is denoted by χ i r ′ ( G ) . In this paper a study has been initiated on edge irredundant coloring of G. We have characterized all graphs G for which χ i r ′ ( G ) = m or m − 1 , where m is the size of a graph G. Also we have obtained some bounds on χ i r ′ for triangle-free graphs and trees.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.016
      Issue No: Vol. 63 (2017)
       
  • Structure of wheel-trees with colourings and domination numbers
    • Authors: H.P. Patil; V. Raja
      Pages: 229 - 236
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): H.P. Patil, V. Raja
      The purpose of this paper is to introduce the wheel-trees, which are the natural extensions of 4-trees studied in [Beineke L. W and Pippert R. E., Properties and characterizations of k-trees, Mathematica., 18, (1971), 141–151; Patil H. P., On the structure of k-trees, J. Comb. Inform & System Sci., 11 (2–4), (1986), 57–64] and also establish the properties and characterizations of the wheel-trees G 〈 W k 〉 for k ≥ 6 . Moreover, the chromatic number, centrality, domination and Roman domination numbers of the wheel-trees of order ≥6 are determined.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.018
      Issue No: Vol. 63 (2017)
       
  • Set Labelling Vertices To Ensure Adjacency Coincides With Disjointness
    • Authors: Mahipal Jadeja; Rahul Muthu; V. Sunitha
      Pages: 237 - 244
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Mahipal Jadeja, Rahul Muthu, V. Sunitha
      Given a set of nonempty subsets of some universal set, their intersection graph is defined as the graph with one vertex for each set and two vertices are adjacent precisely when their representing sets have non-empty intersection. Sometimes these sets are finite, but in many well known examples like geometric graphs (including interval graphs) they are infinite. One can also study the reverse problem of expressing the vertices of a given graph as distinct sets in such a way that adjacency coincides with intersection of the corresponding sets. The sets are usually required to conform to some template, depending on the problem, to be either a finite set, or some geometric set like intervals, circles, discs, cubes etc. The problem of representing a graph as an intersection graph of sets was first introduced by Erdos [Alon, Noga, Covering graphs by the minimum number of equivalence relations, Combinatorica 6(1986), 201–206] and they looked at minimising the underlying universal set necessary to represent any given graph. In that paper it was shown that the problem is NP complete. In this paper we study a natural variant of this problem which is to consider graphs where vertices represent distinct sets and adjacency coincides with disjointness. Although this is nearly the same problem on the complement graph, for specific families of graphs this is a more natural way of viewing it. The parameter we take into account is the minimum universe size possible (disregarding individual label sizes).

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.019
      Issue No: Vol. 63 (2017)
       
  • Edge a-Zagreb Indices and its Coindices of Transformation Graphs
    • Authors: K. Pattabiraman; M. Vijayaragavan
      Pages: 251 - 269
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): K. Pattabiraman, M. Vijayaragavan
      The edge a-Zagreb index and its coindex are defined as Z a ( G ) = ∑ u v ∈ E ( G ) ( d a ( u ) + d ( v ) ) and Z ‾ a ( G ) = ∑ u v ∉ E ( G ) ( d a ( u ) + d a ( v ) ) . In this paper, we obtain the exact expressions for the edge a-Zagreb indices and its coindices of two different transformation of graphs and their complements. Using the results obtained here, the value of F-index and its coindex for above transformation graphs are obtained.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.021
      Issue No: Vol. 63 (2017)
       
  • Incomparability graphs of the lattices Ln and Ln12
    • Authors: Meenakshi Wasadikar; Amit Dabhole
      Pages: 271 - 278
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Meenakshi Wasadikar, Amit Dabhole
      In this paper, we study the incomparability graph of the lattices L n and L n 1 2 . I such graphs, we find minimum dominating set and order of a graph. We express the cardinality of neighbourhood of an atom by a binomial expression.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.022
      Issue No: Vol. 63 (2017)
       
  • Signed Edge Domination Number of Interval Graphs
    • Authors: Angshu Kumar Sinha; Akul Rana; Anita Pal
      Pages: 279 - 286
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Angshu Kumar Sinha, Akul Rana, Anita Pal
      Let G = ( V , E ) be an undirected graph with vertex set V and edge set E. The open neighborhood N(e) of an edge e ∈ E is the set of all edges adjacent to e. The closed neighborhood of e is denoted by N[e] and N [ e ] = N ( e ) ∪ { e } . A function f : E → { 1 , − 1 } is said to be a signed edge dominating function (SEDF), if f satisfies the condition ∑ e ′ ∈ N [ e ] f ( e ′ ) ≥ 1 for every e ∈ E . The minimum of the values of ∑ e ∈ E f ( e ) , taken over all signed edge dominating functions f on G, is called the signed edge domination number (SEDN) of G and is denoted by γ s ′ ( G ) . In this paper, an O ( n 2 ) time algorithm is designed to compute the signed edge domination number of interval graphs.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.023
      Issue No: Vol. 63 (2017)
       
  • Betweenness Centrality in Cartesian Product of Graphs
    • Authors: Sunil Kumar R.; Kannan Balakrishnan
      Pages: 287 - 294
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Sunil Kumar R., Kannan Balakrishnan
      Betweenness centrality is a widely used to measure the potential of a node to control the communication over the network. It measures the extent to which a vertex is part of the shortest paths between pairs of other vertices in a graph. In this paper, we establish expression for betweenness centrality in Cartesian product of graphs. And investigate the same on certain graphs such as Hamming graphs, hypercubes, Cartesian product of path and cycle.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.024
      Issue No: Vol. 63 (2017)
       
  • On the number of geodesics of Petersen graph GP(n,2)
    • Authors: Sunil Kumar R.; Kannan Balakrishnan
      Pages: 295 - 302
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Sunil Kumar R., Kannan Balakrishnan
      For each n and k ( n > 2 k ) , the generalized Petersen graph GP (n, k) is a trivalent graph with vertex set { u i , v i 0 ≤ i ≤ n − 1 } and edge set { u i u i + 1 , u i v i , v i v i + k 0 ≤ i ≤ n − 1 ,  subscripts reduced modulo  n } . There are three kinds of edges – outer edges, spokes and inner edges. Outer vertices generate an n-cycle called outer cycle and the inner vertices generate one or more cycles called inner cycles. In this paper, we consider the number of shortest paths or geodesics between two vertices of GP (n, 2).

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.025
      Issue No: Vol. 63 (2017)
       
  • Trees with minimum F-coindex
    • Authors: Ruhul Amin; Sk. Md. Abu Nayeem
      Pages: 303 - 310
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Ruhul Amin, Sk. Md. Abu Nayeem
      The F-coindex of a graph G is a very recently introduced topological index, and it is defined as the sum of the square of the degrees of every pair of non-adjacent vertices. In this paper, we determine the extremal trees with minimum, second minimum and third minimum F-coindex.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.026
      Issue No: Vol. 63 (2017)
       
  • Some Distance Magic Graphs
    • Authors: Aloysius Godinho; T. Singh
      Pages: 311 - 315
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Aloysius Godinho, T. Singh
      Let G = (V, E) be a graph of order n. A bijective function f : V → { 1 , 2 , … , n } is said to be a distance magic labeling of G if for every v ∈ V , ∑ x ∈ N ( v ) f ( x ) = k (a constant). A graph which admits such a labeling is said to be a distance magic graph. In this paper we study distance magic labeling for the neighborhood expansion D p ( G ) of a graph G and present a method for embedding regular graphs into distance magic graphs.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.027
      Issue No: Vol. 63 (2017)
       
  • Distance Antimagic Labeling of the Ladder Graph
    • Authors: A.K. Handa; Aloysius Godinho; T. Singh
      Pages: 317 - 322
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): A.K. Handa, Aloysius Godinho, T. Singh
      Let G be a graph of order n. Let f : V ( G ) → { 1 , 2 , … , n } be a bijection. The weight w f ( v ) of a vertex with respect to f is defined by w f ( v ) = ∑ x ∈ N ( v ) f ( x ) . The labeling f is said to be distance antimagic if w f ( u ) ≠ w f ( v ) for every pair of vertices u , v ∈ V ( G ) . If the graph G admits such a labeling then G is said to be a distance antimagic graph. In this paper we investigate the existence of distance antimagic labeling in the ladder graph L n ≅ P 2 □ P n .

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.028
      Issue No: Vol. 63 (2017)
       
  • An Algorithmic Characterization of Splitting Signed Graph
    • Authors: Deepa Sinha; Anshu Sethi
      Pages: 323 - 332
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Deepa Sinha, Anshu Sethi
      A signed graph (also known as sigraph) S is a graph G ′ where every edge y have value s ′ ( y ) ∈ { − 1 , + 1 } known as its sign function and is denoted as S = ( G ′ , s ′ ) . Given a sigraph S = ( V , E , σ ) , for every vertex v ∈ V ( S ) , take a new vertex v ′ . Join v ′ to all vertices of S adjacent to v such that, σ Λ ( u v ′ ) = σ ( u v ) , u ∈ N ( v ) . The sigraph Λ ( S ) = ( V Λ , E Λ , σ Λ ) thus produced is called the splitting sigraph of S. Here we define an algorithm to produce a splitting sigraph and root splitting sigraph from a given sigraph, if it exists, in O ( n 4 ) steps.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.029
      Issue No: Vol. 63 (2017)
       
  • On self-centeredness of tensor product of some graphs
    • Authors: Priyanka Singh; Pratima Panigrahi
      Pages: 333 - 342
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Priyanka Singh, Pratima Panigrahi
      A simple connected graph G is said to be a self-centered graph if every vertex has the same eccentricity. Tensor product of self-centered graphs may not be a self-centered graph. In this paper we study self-centeredness property of tensor product of cycles with themselves and other graphs, complete graphs with themselvesand other self-centered graphs, wheel graphs with themselves and other self-centered graphs, and square of cycles with themselves.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.030
      Issue No: Vol. 63 (2017)
       
  • L(2,1)-colorings and Irreducible No-hole Colorings of Cartesian Product of
           Graphs
    • Authors: Nibedita Mandal; Pratima Panigrahi
      Pages: 343 - 352
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Nibedita Mandal, Pratima Panigrahi
      An L ( 2 , 1 ) -coloring(or labeling) of a graph G is a mapping f : V ( G ) → Z + ⋃ { 0 } such that f ( u ) − f ( v ) ≥ 2 for all edges uv of G, and f ( u ) − f ( v ) ≥ 1 if d ( u , v ) = 2 , where d ( u , v ) is the distance between vertices u and v in G. The span of an L ( 2 , 1 ) -coloring is the maximum color assigned by it. The span of a graph G, denoted by λ ( G ) , is the smallest positive integer λ such that there is an L ( 2 , 1 ) coloring of G using colors from { 0 , ⋯ , λ } . A no-hole coloring is defined to be an L ( 2 , 1 ) -coloring of a graph with span k which uses all the colors from { 0 , 1 , ⋯ , k } for some integer k not necessarily the span of the graph. An L ( 2 , 1 ) -coloring is defined as irreducible if color of none of the vertices can be decreased and yield another L ( 2 , 1 ) -coloring of the same graph. An irreducible no-hole coloring of a graph G, in short inh-coloring of G, is an L ( 2 , 1 ) -coloring of G which is both irreducible and no-hole. The lower inh-span or simply inh-span of a graph G, denoted by λ i n h ( G ) , is the smallest integer k such that there exists an inh-coloring of G with span k. In this paper we work on the L ( 2 , 1 ) -coloring and inh-coloring of the Cartesian product K m □ C n of complete graphs and cycles and find the exact values of λ ( K m □ C n ) and λ i n h ( K m □ C n ) for some values of m and n, and give upper bounds to the same in the remaining cases. We also give two upper bounds of the span of the Cartesian product of two arbitrary graphs which are better than the upper bound of Shao and Yeh [Sha...
      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.031
      Issue No: Vol. 63 (2017)
       
  • Polynomial Time Efficient Construction Heuristics for Vertex Separation
           Minimization Problem
    • Authors: Pallavi Jain; Gur Saran; Kamal Srivastava
      Pages: 353 - 360
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Pallavi Jain, Gur Saran, Kamal Srivastava
      Vertex Separation Minimization Problem (VSMP) consists of finding a layout of a graph G = (V, E) which minimizes the maximum vertex cut or separation of a layout. It is an NP-complete problem in general for which metaheuristic techniques can be applied to find near optimal solution. VSMP has applications in VLSI design, graph drawing and computer language compiler design. VSMP is polynomially solvable for grids, trees, permutation graphs and cographs. Construction heuristics play a very important role in the metaheuristic techniques as they are responsible for generating initial solutions which lead to fast convergence. In this paper, we have proposed three construction heuristics H1, H2 and H3 and performed experiments on Grids, Small graphs, Trees and Harwell Boeing graphs, totaling 248 instances of graphs. Experiments reveal that H1, H2 and H3 are able to achieve best results for 88.71%, 43.5% and 37.1% of the total instances respectively while the best construction heuristic in the literature achieves the best solution for 39.9% of the total instances. We have also compared the results with the state-of-the-art meta-heuristic GVNS and observed that the proposed construction heuristics improves the results for some of the input instances. It was found that GVNS obtained best results for 82.9% instances of all input instances and the heuristic H1 obtained best results for 82.3% of all input instances.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.032
      Issue No: Vol. 63 (2017)
       
  • Layout of embedding locally twisted cube into the extended theta mesh
           topology
    • Authors: Jessie Abraham; Micheal Arockiaraj
      Pages: 371 - 379
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Jessie Abraham, Micheal Arockiaraj
      A graph embedding is an important aspect in establishing equivalence of interconnections in parallel and distributed machines. Finding the minimum layout serves as a cost criterion for evaluating a good embedding. The binary hypercube is one of the most widely used topology for interconnection networks due to its simple, deadlock-free routing and broadcasting properties. The locally twisted cube is an important variant of the hypercube with the same number of vertices and connections but exhibits enhanced properties than its counterpart. In this paper we consider the problem of embedding an n-dimensional locally twisted cube into the extended rooted theta mesh in such a way as to minimize its layout.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.034
      Issue No: Vol. 63 (2017)
       
  • Minimizing Profile of Graphs Using a Hybrid Simulating Annealing Algorithm
    • Authors: Yogita Singh Kardam; Kamal Srivastava; Reeti Sharma
      Pages: 381 - 388
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Yogita Singh Kardam, Kamal Srivastava, Reeti Sharma
      The profile minimization problem is a graph layout problem that consists of finding a linear arrangement (labeling) of vertices of a graph such that the sum of profiles of all vertices is minimum. The profile of a vertex can be defined as the difference of the position of its left most neighbor and the position of that vertex in the linear arrangement. It is an NP-complete problem with applications in the areas where the reordering of rows and columns of a sparse matrix is required in order to reduce the storage space. In this work, we propose a hybrid simulated annealing algorithm with the aim of profile reduction of a given graph by incorporating spectral sequencing for generating the initial solution. Experiments conducted on some benchmark graphs show that our algorithm outperforms the best existing algorithm in some cases and is comparable for rest of the instances. It also attains the optimal values for some classes of graphs with known optimal results.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.035
      Issue No: Vol. 63 (2017)
       
  • Line Signed Graph of a Signed Total Graph
    • Authors: Mukti Acharya; Pranjali; Atul Gaur; Amit Kumar
      Pages: 389 - 397
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Mukti Acharya, Pranjali, Atul Gaur, Amit Kumar
      A signed total graph is an ordered pair T Σ ( Γ ( R ) ) : = ( T ( Γ ( R ) ) , σ ) , where T ( Γ ( R ) ) is the total graph of a commutative ring R, called the underlying graph of T Σ ( Γ ( R ) ) and T Σ ( Γ ( R ) ) is associated with a signing of its edges (a, b) by the function σ such that σ ( a , b ) is ‘+’ if a ∈ Z ( R ) or b ∈ Z ( R ) and ‘−’ otherwise. The aim of this paper is to gain a deeper insight into the notion of signed total graph by characterizing the rings for which line signed graph L ( T Σ ( Γ ( R ) ) ) of signed total graph are C-consistent, T Σ ( Γ ( R ) ) -consistent and sign-compatible.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.036
      Issue No: Vol. 63 (2017)
       
  • Adjacency Matrix of a Semigraph
    • Authors: Y.S. Gaidhani; C.M. Deshpande; B.P. Athawale
      Pages: 399 - 406
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Y.S. Gaidhani, C.M. Deshpande, B.P. Athawale
      Semigraph was defined by Sampathkumar as a generalization of a graph. In this paper the adjacency matrix which represents semigraph uniquely and a characterization of such a matrix is obtained. An algorithm to construct the semigraph from a given square matrix, if semigraphical is given. Some properties of adjacency matrix of semigraph are studied. A sufficient condition for eigen values to be real is also obtained.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.037
      Issue No: Vol. 63 (2017)
       
  • b-Chromatic Sum of Mycielskian of Paths
    • Authors: P.C. Lisna; M.S. Sunitha
      Pages: 407 - 414
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): P.C. Lisna, M.S. Sunitha
      A b-coloring of a graph G is a proper coloring of the vertices of G such that there exist a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph G, denoted by ϕ ( G ) , is the largest integer k such that G has a b-coloring with k colors. The b-chromatic sum of a graph G(V, E), denoted by ϕ ′ ( G ) is defined as the minimum of sum of colors c(v) of v for all v ∈ V in a b-coloring of G using ϕ ( G ) colors, where the colors are taken as the positive integer. In this paper, the b-chromatic sum of Mycielskian of a path is discussed.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.038
      Issue No: Vol. 63 (2017)
       
  • Minimum Geodetic Fuzzy Subgraph
    • Authors: Sameeha Rehmani; M.S. Sunitha
      Pages: 415 - 424
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Sameeha Rehmani, M.S. Sunitha
      The concept of Minimum geodetic subgraphs in Graph theory was introduced by G. Chartrand, F. Harary and P. Zhang in 2001. In this paper,the idea is extended to fuzzy graphs using geodesic distance.An upper and lower bound for geodesic number of fuzzy graphs is obtained using which it is established that the geodesic number of a fuzzy graph exceeds or is equal to that of its minimum geodetic fuzzy subgraph. A necessary condition for the geodesic number of a fuzzy graph to be 2 depending on the nodes of its minimum geodetic fuzzy subgraph is obtained and a study on the minimum geodetic fuzzy subgraph of a fuzzy tree is conducted.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.039
      Issue No: Vol. 63 (2017)
       
  • Unitary Cayley Meet Signed Graphs
    • Authors: Deepa Sinha; Ayushi Dhama
      Pages: 425 - 434
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): Deepa Sinha, Ayushi Dhama
      A signed graph S is a graph in which every edge receive either ‘+’ or ‘-’ called the signs of the edges. The unitary Cayley graph X n is a graph with vertex set Z n , the integers modulo n, where n is a positive integer greater than 1. Two vertices x 1 and x 2 are adjacent in the unitary Cayley graph if and only if their difference is in U n , where U n denotes set of all units of the ring Z n . The properties of balancing and clusterability of unitary Cayley meet signed graph S n ∧ are discussed. Apart from this, the canonically consistency of S n ∧ is determined when n has at most two distinct odd prime factors. Sign-compatibility has been worked out for these graphs as well.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.040
      Issue No: Vol. 63 (2017)
       
  • On the Metric Dimension of Join of a Graph with Empty Graph(Op)
    • Authors: A.T. Shahida; M.S. Sunitha
      Pages: 435 - 445
      Abstract: Publication date: December 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 63
      Author(s): A.T. Shahida, M.S. Sunitha
      For a graph G = (V, E), a set W ⊂ V is a resolving set if for each pair of distinct vertices v 1 , v 2 ∈ V there is a vertex w ∈ W such that d ( v 1 , w ) ≠ d ( v 2 , w ) . A minimum resolving set or basis for G is a resolving set containing a minimum number of vertices and the cardinality of a minimum resolving set is called the metric dimension of G and is denoted by dim(G). In this paper, we investigates the metric dimension of K n + O p , P n + O p and K 1 , n + O p , where O p denotes the empty (isolated) graph of order p.

      PubDate: 2017-12-13T09:16:42Z
      DOI: 10.1016/j.endm.2017.11.041
      Issue No: Vol. 63 (2017)
       
 
 
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