Results 21 to 30 of about 8,253 (248)
The total co-independent domination number of some graph operations [PDF]
, 2022 [EN] A set D of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex of D. The total dominating set D is called a total co-independent dominating set if the subgraph induced by V (G)- D is edgeless.
González Yero, Ismael +4 more
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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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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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Remarks on the outer-independent double Italian domination number
, 2021 Let $G$ be a graph with vertex set $V(G)$. If $u \in V(G)$, then $N[u]$ is the closed neighborhood of $u$. An outer-independent double Italian dominating function (OIDIDF) on a graph $G$ is a function $ƒ : V(G) \rightarrow \{0, 1, 2, 3\}$ such that if $ƒ
Volkman, Lutz, Volkmann, Lutz
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Independent strong domination number of indu-bala product of graphs
, 2023 A set D⊂ V be the strong dominating set of G if every vertex in V − D is strongly dominated by at least one vertex in D. The strong domination number γst(G) of G is the minimum cardinality of a strong dominating set.
Priyadharshini M. +2 more
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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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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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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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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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On the outer-independent double Italian domination number
Electronic Journal of Graph Theory and Applications, 2022 Summary: An outer-independent Italian dominating function (OIIDF) on a graph \(G\) is a function \(f : V(G)\longrightarrow \{0, 1, 2\}\) such that every vertex \(v\in V(G)\) with \(f(v)=0\) has at least two neighbors assigned 1 under \(f\) or one neighbor \(w\) with \(f(w)=2\), and the set \(\{u \in V(G)|f(u)=0\}\) is independent.
Noor A'lawiah Abd Aziz +3 more
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