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Paired Domination Vertex Critical Graphs
Graphs and Combinatorics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hou, Xinmin, Edwards, Michelle
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2020
A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The minimum cardinality of a paired dominating set of G is the paired domination number of G.
Desormeaux, Wyatt J. +2 more
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A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The minimum cardinality of a paired dominating set of G is the paired domination number of G.
Desormeaux, Wyatt J. +2 more
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Networks, 1998
Summary: In a graph \(G= (V,E)\) if we think of each vertex \(s\) as the possible location for a guard capable of protection each vertex in its closed neighborhood \(N[s]\), then ``domination'' requires every vertex to be protected. Thus, \(S\subset V(G)\) is a dominating set if \(\bigcup_{s\in s}N[s]= V(G)\).
Haynes, Teresa W., Slater, Peter J.
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Summary: In a graph \(G= (V,E)\) if we think of each vertex \(s\) as the possible location for a guard capable of protection each vertex in its closed neighborhood \(N[s]\), then ``domination'' requires every vertex to be protected. Thus, \(S\subset V(G)\) is a dominating set if \(\bigcup_{s\in s}N[s]= V(G)\).
Haynes, Teresa W., Slater, Peter J.
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Journal of Combinatorial Optimization, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fitzpatrick, S. L., Hartnell, B. L.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fitzpatrick, S. L., Hartnell, B. L.
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Complexity of Paired Domination in AT-free and Planar Graphs
International Conference on Algorithms and Discrete Applied Mathematics, 2021For a graph $G=(V,E)$, a subset $D$ of vertex set $V$, is a dominating set of $G$ if every vertex not in $D$ is adjacent to atleast one vertex of $D$. A dominating set $D$ of a graph $G$ with no isolated vertices is called a paired dominating set (PD-set)
Vikash Tripathi +4 more
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Outer-paired domination in graphs
Discrete Mathematics, Algorithms and Applications, 2020Let [Formula: see text] be a simple graph with vertex set [Formula: see text] and edge set [Formula: see text]. An outer-paired dominating set [Formula: see text] of a graph [Formula: see text] is a dominating set such that the subgraph induced by [Formula: see text] has a perfect matching.
A. Mahmoodi, L. Asgharsharghi
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Paired domination in graphs with minimum degree four
Discrete MathematicsA set $S$ of vertices in a graph $G$ is a paired dominating set if every vertex of $G$ is adjacent to a vertex in $S$ and the subgraph induced by $S$ admits a perfect matching.
Csilla Bujt'as, Michael A. Henning
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Paired-Domination Subdivision Numbers of Graphs
Graphs and Combinatorics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Favaron, O. +2 more
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Eternal Paired Domination in Graphs
Discrete Mathematics, Algorithms and Applications (DMAA)Eternal domination of a graph requires the vertices of the graph to be protected, against infinitely long sequences of attacks, by guards located at vertices (at most one guard at each vertex), with the requirement that the configuration of guards ...
D. Yokesh, P. R. L. Pushpam, G. Navamani
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Paired-Domination in Claw-Free Graphs
Graphs and Combinatorics, 2012A paired-dominating set of a graph \(G\) is a dominating set \(S\) of vertices such that there exists a perfect matching in the subgraph induced by \(S\). The paired-domination number, denoted by \(\gamma_{pr}(G)\), is the minimum cardinality of a paired-dominating set in \(G\).
Huang, Shenwei +2 more
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