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Total Domination Versus Paired-Domination in Regular Graphs
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph
Cyman Joanna +4 more
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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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Block Graphs with Large Paired Domination Multisubdivision Number
Discussiones Mathematicae Graph Theory, 2021 The paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G.
Mynhardt Christina M., Raczek Joanna
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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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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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Parameterized Complexity of Paired Domination [PDF]
The Paired Domination problem is one of the well-studied variants of the classical Dominating Set problem. In a graph G on nvertices, a dominating set D (set of vertices such that N[D] = V (G)) is called a paired dominating set of G, if G[D] has perfect ...
Tripathi, Vikash +5 more
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, 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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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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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
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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
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