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On graphs whose domination numbers equal their independent domination numbers
Electronic Notes in Discrete Mathematics, 2003 Abstract In this paper, we extend a result due to R. B. Allan and R. C. Laskar on graphs whose independent domination numbers equal their domination numbers. We will consider finite simple graphs as treated in most of the standard text-books on Graph Theory (e.g., see D. B. West [1]). Let G = (V,E) be any graph and D ⊆ V. We let N(D) denote the set
Belmannu Devadas Acharya, Purnima Gupta
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On Independent Domination in Planar Cubic Graphs
Discussiones Mathematicae Graph Theory, 2019 A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S.
Abrishami Gholamreza +2 more
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On the Total Outer k-Independent Domination Number of Graphs
Mathematics, 2020 A set of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex in such a set. We say that a total dominating set D is a total outer k-independent dominating set of G if the maximum degree of the subgraph ...
Abel Cabrera-Martínez +3 more
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An upper bound on the total outer-independent domination number of a tree [PDF]
Opuscula Mathematica, 2012 A total outer-independent dominating set of a graph \(G=(V(G),E(G))\) is a set \(D\) of vertices of \(G\) such that every vertex of \(G\) has a neighbor in \(D\), and the set \(V(G) \setminus D\) is independent.
Marcin Krzywkowski
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Changing and Unchanging 2-Rainbow Independent Domination
IEEE Access, 2019 Domination number is of practical interest in several theoretical and applied scenes. In the problem of wireless networking, the dominating idea is used to deduce an efficient route within the adhoc mobilenetworks.
Xiaolong Shi +6 more
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On the Number of k‐Dominating Independent Sets [PDF]
Journal of Graph Theory, 2016 AbstractWe study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erdős and Moser—is widely investigated, much less is known in general.
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Independent Domination Number of Operation Graph
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS, 2020 Let G be a simple, undirected and connected graph. An independent set or stable set is a set of vertices in a graph in which no two of vertices are adjacent. A set D of vertices of graph G is called a dominating set if every vertex u ∈ V (G) − D is adjacent to some vertex v ∈ D.
Siti Aminatus Solehah +2 more
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On graphs with equal domination and independent domination numbers
Discrete Mathematics, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Topp, Jerzy, Volkmann, Lutz
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A note on the independent domination number versus the domination number in bipartite graphs [PDF]
Czechoslovak Mathematical Journal, 2017 Accepted by Czechoslovak Mathematical ...
Wang, Shaohui, Wei, Bing
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On domination and independent domination numbers of a graph
Discrete Mathematics, 1978 AbstractFor a graph G, the definitions of domination number, denoted γ(G), and independent domination number, denoted i(G), are given, and the following results are obtained:Theorem. If G does not have an induced subgraph isomorphic to K1,3, then γ(G) = i(G).Corollary 1. For any graph G, γ(L(G))=i(L(G)), where L(G) is the line graph of G. (This extends
Allan, Robert B., Laskar, Renu
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