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Paired-Domination Subdivision Numbers of Graphs
Graphs and Combinatorics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seyed Mahmoud Sheikholeslami +2 more
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Total domination versus paired domination [PDF]
, 2011 A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by gamma_t .
Schaudt, Oliver
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Paired-domination game played on cycles
Discrete Applied Mathematics, 2023This text further develops the graph domination game introduced in [\textit{B. Brešar} et al. SIAM J. Discrete Math. 24, No. 3, 979--991 (2010; Zbl 1223.05189)]. The version of the game studied involves two players, the Dominator and the Staller, who take turns choosing pairs of adjacent, unchosen vertices that dominate at least one vertex not ...
Michael Henning
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Trees with Equal Domination and Paired-domination Numbers.
Ars Comb., 2005 A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G is the minimum cardinality of a paired-dominating set of G, and is obviously bounded below by the domination number of G.
Haynes, Teresa W. +2 more
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On paired and double domination in graphs
, 2005 Summary: A paired dominating set of a graph \(G\) is a dominating set of vertices whose induced subgraph has a perfect matching, and a double dominating set is a dominating set that dominates every vertex of \(G\) at least twice. First a necessary and sufficient condition is given for a double dominating set (respectively, paired dominating set) to be ...
Chellali, Mustapha, Haynes, Teresa W.
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Upper total domination versus upper paired-domination
Quaestiones Mathematicae, 2007 Let G be a graph with no isolated vertices. A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S, while a paired-dominating set of G is a dominating set of vertices whose induced subgraph has a ...
Michael Henning, Paul Dorbec
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The Outer-Paired Domination of Graphs
International Journal of Foundations of Computer Science, 2022In this paper, we introduce a new variant of domination called the outer-paired domination. For a graph [Formula: see text], an outer-paired dominating set [Formula: see text] is a dominating set of [Formula: see text] such that the induced subgraph of [Formula: see text] contains a perfect matching.
Chih-Yuan Lin +4 more
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Characterizations of trees with equal paired and double domination numbers [PDF]
Discrete Mathematics, 2006 A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching, and a double dominating set is a dominating set that dominates every vertex of G at least twice.
Mustapha Chellali, Teresa Haynes
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Journal of Global Optimization, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong Qiao +3 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong Qiao +3 more
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SIAM Journal on Discrete Mathematics, 2002
Summary: A pair of vertices of a graph is called a dominating pair if the vertex set of every path between these two vertices is a dominating set of the graph. A graph is a weak dominating pair graph if it has a dominating pair. Further, a graph is called a dominating pair graph if each of its connected induced subgraphs is a weak dominating pair graph.
Jitender S. Deogun, Dieter Kratsch
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Summary: A pair of vertices of a graph is called a dominating pair if the vertex set of every path between these two vertices is a dominating set of the graph. A graph is a weak dominating pair graph if it has a dominating pair. Further, a graph is called a dominating pair graph if each of its connected induced subgraphs is a weak dominating pair graph.
Jitender S. Deogun, Dieter Kratsch
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