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Domination Number, Independent Domination Number and 2-Independence Number in Trees [PDF]
Discussiones Mathematicae Graph Theory, 2021 For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees ...
Dehgardi Nasrin +4 more
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Algorithmic Aspects of the Independent 2-Rainbow Domination Number and Independent Roman {2}-Domination Number [PDF]
Discussiones Mathematicae Graph Theory, 2022 A 2-rainbow dominating function (2RDF) of a graph G is a function g from the vertex set V (G) to the family of all subsets of {1, 2} such that for each vertex v with g(v) =∅ we have ∪u∈N(v) g(u) = {1, 2}.
Poureidi Abolfazl, Rad Nader Jafari
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Independent [1,2]-number versus independent domination number [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 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 ...
Aleid Sahar A. +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.
Purnima Gupta, Rajesh Singh, S. Arumugam
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Remarks on the outer-independent double Italian domination number [PDF]
Opuscula Mathematica, 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 \(f:V(G)\longrightarrow \{0,1,2,3\}\) such
Lutz Volkmann
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A note on the independent domination number of subset graph [PDF]
Czechoslovak Mathematical Journal, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Xuegang +3 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 outer-independent double Italian domination number
Electronic Journal of Graph Theory and Applications, 2022 An outer-independent Italian dominating function (OIIDF) on a graph G is a function f : V(G)→{0, 1, 2} such that every vertex v ∈ 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 ∈ V(G)|f(u)=0}
Noor A'lawiah Abd Aziz +3 more
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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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On the Total Outer k-Independent Domination Number of Graphs [PDF]
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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