Results 1 to 10 of about 8,253 (248)
Domination, independent domination number and 2-independence number in trees
Discussiones Mathematicae Graph Theory, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dehgardi Nasrin +4 more
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Independent [1,2]-number versus independent domination number [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2017 Abstract A [1; 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and at most two neighbors in it. If the additional requirement that the set be independent is added, the existence of such sets is not guaranteed in every graph. In this paper we provide local conditions, depending on the degree of
Aleid, Sahar A. +2 more
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On domination and independent domination numbers of a graph [PDF]
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
Robert B. Allan, Renu C. Laskar
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On the ratio of the domination number and the independent domination number in graphs
Discrete Applied Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michitaka Furuya, Kenta Ozeki
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A note on the independent domination number in graphs
Discrete Applied Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nader Jafari Rad, Lutz Volkmann
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On the Independent Domination Number of Regular Graphs
Annals of Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wayne Goddard +2 more
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Graphs with equal domination and independent domination numbers [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 Let γ(G) and i(G) denote the domination number and independent domination number of a graph G. In this article, we establish a sufficient condition for a graph G to satisfy which yields some of the well known classical theorems as corollaries. Further, we also construct several families of graphs G satisfying γ(G) = i(G) using the sufficient condition.
Purnima Gupta +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.
Jerzy Topp, Lutz Volkmann
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Graphs with equal Grundy domination and independence number
Discrete Optimization, 2023 The Grundy domination number, ${γ_{\rm gr}}(G)$, of a graph $G$ is the maximum length of a sequence $(v_1,v_2,\ldots, v_k)$ of vertices in $G$ such that for every $i\in \{2,\ldots, k\}$, the closed neighborhood $N[v_i]$ contains a vertex that does not belong to any closed neighborhood $N[v_j]$, where ...
Gábor Bacsó +3 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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