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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).
Haynes, Teresa W. +5 more
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Paired-domination in inflated graphs
Theoretical Computer Science, 2004 The inflation GI of a graph G with n(G) vertices and m(G) edges is obtained from G by replacing every vertex of degree d of G by a clique Kd. A set S of vertices in a graph G is a paired dominating set of G if every vertex of G is adjacent to some vertex
Cheng, TCE +5 more
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Graphs with disjoint dominating and paired-dominating sets
Open Mathematics, 2010 Abstract A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching.
Southey Justin, Henning Michael
doaj +3 more sources
Characterizations of trees with equal paired and double domination numbers
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.
Mostafa Blidia +2 more
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Distance paired domination numbers of graphs
Discrete Mathematics, 2008 In this paper, we study a generalization of the paired domination number. Let G=(V,E) be a graph without an isolated vertex. A set D⊆V(G) is a k-distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has
Raczek, Joanna
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Paired-domination of Cartesian products of graphs and rainbow domination
Electronic Notes in Discrete Mathematics, 2005 Abstract The most famous open problem involving domination in graphs is Vizing's conjecture which states the domination number of the Cartesian product of any two graphs is at least as large as the product of their domination numbers. We investigate a similar problem for paired-domination, and obtain a lower bound in terms of product of domination ...
Boštjan Brešar +2 more
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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 ...
Paul Dorbec, Michael A Henning
exaly +1 more source
Perfectly relating the domination, total domination, and paired domination numbers of a graph
Discrete Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Simone Dantas, Dieter Rautenbach
exaly +3 more sources
, 2013 D.Phil. (Mathematics)Domination and its variants are now well studied in graph theory. One of these variants, paired-domination, requires that the subgraph induced by the dominating set contains a perfect matching.
McCoy, John Patrick
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Induced-Paired Domination in Graphs
Ars Comb., 2000 For a graph G = (V, E), a set S ⊆ V is a dominating set if every vertex in V - S is adjacent to at least one vertex in S. A dominating set S ⊆ V is a paired-dominating set if the induced subgraph 〈S〉 has a perfect matching.
Haynes, Teresa W. +2 more
core +2 more sources