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Open Journal of Discrete Mathematics (OJDM) is an openly accessible journal published quarterly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote,share,and discuss various new issues and developments in different areas of discrete mathematics. All manuscri…
Bing Zhou
We investigate the dominating- c -color number, , of a graph G . That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graph…
Nazanin Movarraei, Samina A. Boxwala
In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v i in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.
Vladimir Leontiev, Garib Movsisyan, Zhirayr Margaryan
In the present paper, geometry of the Boolean space B n in terms of Hausdorff distances between subsets and subset sums is investigated. The main results are the algebraic and analytical expressions for representing of classical figures in B n and the functio…
Ruzayn Quaddoura
The bipartite Star 123 -free graphs were introduced by V. Lozin in [1] to generalize some already known classes of bipartite graphs. In this paper, we extend to bipartite Star 123 -free graphs a linear time algorithm of J. L. Fouquet, V. Giakoumakis and J. M.…
Ramadan El-Shanawany
A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G . Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of i…
Paul A. Burchett
The question associated with total domination on the queen’s graph has a long and rich history, first having been posed by Ahrens in 1910 [1]. The question is this: What is the minimum number of queens needed so that every square of an n × n board is attacked…
Morteza Alishahi, Sakineh Hoseini Shalmaee
A set is a dominating set of G if every vertex of is adjacent to at least one vertex of S . The cardinality of the smallest dominating set of G is called the domination number of G . The square G 2 of a graph G is obtained from G by adding new edges between e…
A. Vijayan, J. Sherin Beula
Let G = ( V , E ) be a simple graph. A set S E ( G ) is an edge-vertex dominating set of G (or simply an ev -dominating set), if for all vertices v V ( G ); there exists an edge e S such that e dominates v . Let denote the family of all ev -dominating sets of…
Steven J. Tedford
Fuzzy greedoids were recently introduced as a fuzzy set generalization of (crisp) greedoids. We characterize fuzzy languages which define fuzzy greedoids, give necessary properties and sufficient properties of the fuzzy rank function of a fuzzy greedoid, give…
Ramy Shaheen
Let D be a finite simple directed graph with vertex set V ( D ) and arc set A ( D ). A function is called a signed dominating function (SDF) if for each vertex . The weight of f is defined by . The signed domination number of a digraph D is . Let C m × C n de…
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Open Journal of Discrete Mathematics (OJDM) is an openly accessible journal published quarterly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote,share,and discuss various new issues and developments in different areas of discrete mathematics. All manuscri… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
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