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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
B. 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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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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Independent partial domination
Cubo, 2021 For $p\in(0,1]$, a set $S\subseteq V$ is said to $p$-dominate or partially dominate a graph $G = (V, E)$ if $\frac{|N[S]|}{|V|}\geq p$. The minimum cardinality among all $p$-dominating sets is called the $p$-domination number and it is denoted by ...
L. Philo Nithya +1 more
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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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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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Domination and independence subdivision numbers of graphs
Discussiones Mathematicae Graph Theory, 2000 A subset \(S\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). A set \(S\subseteq V(G)\) is independent in \(G\), if no two vertices of \(S\) are adjacent in \(G\).
Teresa W. Haynes +2 more
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A note on domination and independence-domination numbers of graphs
Ars Mathematica Contemporanea, 2012 Vizing's conjecture is true for graphs G satisfying γ i ( G ) = γ ( G ), where γ ( G ) is the domination number of a graph G and γ i ( G ) is the independence-domination number of G , that is, the maximum, over all independent sets I in G , of the minimum number of vertices needed to dominate I . The equality γ i ( G ) = γ (
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Independent Dominator Sequence Number of a Graph
Procedia Computer Science, 2015 AbstractLet G = (V, E) be a connected graph. A dominator sequence in G is a sequence of vertices S = (v1, v2,. . ., vk) such that for each i with 2 ≤ i ≤ k, the vertex vi dominates at least one vertex which is not dominated by v1, v2,. . ., vi−1. If further the set of vertices in S is an independent set, then S is called an independent dominator ...
S. Arumugam 0001 +2 more
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An improvement on the maximum number of ‐dominating independent sets [PDF]
Journal of Graph Theory, 2018 AbstractErdős and Moser raised the question of determining the maximum number of maximal cliques or, equivalently, the maximum number of maximal independent sets in a graph on vertices. Since then there has been a lot of research along these lines.A ‐dominating independent set is an independent set such that every vertex not contained in has at ...
Dániel Gerbner +4 more
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