Results 11 to 20 of about 9,176,317 (295)
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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On the equality of domination number and 2-domination number [PDF]
Discussiones Mathematicae Graph TheoryThe 2-domination number $γ_2(G)$ of a graph $G$ is the minimum cardinality of a set $ D \subseteq V(G) $ for which every vertex outside $ D $ is adjacent to at least two vertices in $ D $. Clearly, $ γ_2(G) $ cannot be smaller than the domination number $ γ(G) $.
Gülnaz Boruzanlı Ekinci +1 more
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Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees [PDF]
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S.
Rad Nader Jafari, Rahbani Hadi
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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 domination multisubdivision number of unicyclic graphs [PDF]
Opuscula Mathematica, 2018 The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram,
Joanna Raczek
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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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Total Domination Multisubdivision Number of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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Discrete Mathematics, 2002 The dominating set of a digraph \(D\) is a set \(S\) of vertices such that for every \(v\not\in S\) there exists \(u\in S\) with \(uv\in A(D)\). The domination number of \(D\) is the cardinality of the smallest dominating set. The game domination number of an undirected graph \(G\) is the domination number of the digraph \(D\) obtained as a result of ...
Noga Alon +3 more
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Discussiones Mathematicae Graph Theory, 2014 Let K3n denote the Cartesian product Kn□Kn□Kn, where Kn is the complete graph on n vertices.
Georges John, Lin Jianwei, Mauro David
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The Slater and Sub-k-Domination Number of a Graph with Applications to Domination and k-Domination [PDF]
Discussiones Mathematicae Graph Theory, 2020 In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G).
Amos David +3 more
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