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Paired domination in prisms of graphs
Discussiones Mathematicae Graph Theory, 2011 The paired domination number $γ_{pr}(G)$ of a graph G is the smallest cardinality of a dominating set S of G such that ⟨S⟩ has a perfect matching. The generalized prisms πG of G are the graphs obtained by joining the vertices of two disjoint copies of G ...
Mynhardt, Christina, Schurch, Mark
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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 ...
Haynes, Teresa W. +2 more
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Hardness results and approximation algorithms for (weighted) paired-domination in graphs
Theoretical Computer Science, 2009 Let G=(V,E) be a simple graph without isolated vertices. A vertex set S⊆V is a paired-dominating set if every vertex in V−S has a neighbor in S and the induced subgraph G[S] has a perfect matching. In this paper, we investigate the approximation hardness
Changhong Lu, Zhenbing Zeng
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On Paired and Double Domination in Graphs
, 2005 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.
Haynes, Teresa W., Chellali, Mustapha
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Paired disjunctive domination in some shadow distance graphs
Discrete Mathematics, Algorithms and Applications (DMAA)This paper investigates the concept of paired disjunctive domination, initially proposed by Henning et al. A subset D ⊆ V is defined as a disjunctive dominating set of a graph G if, for every vertex v ∈ V, there exists either a vertex in D adjacent to v,
Aytac, Aysun, Golpek, Hande Tuncel
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γ-paired dominating graphs of cycles [PDF]
Opuscula Mathematica, 2022 A paired dominating set of a graph \(G\) is a dominating set whose induced subgraph contains a perfect matching. The paired domination number, denoted by \(\gamma_{pr}(G)\), is the minimum cardinality of a paired dominating set of \(G\).
Pannawat Eakawinrujee +1 more
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All graphs with paired-domination number two less than their order [PDF]
Opuscula Mathematica, 2013 Let \(G=(V,E)\) be a graph with no isolated vertices. A set \(S\subseteq V\) is a paired-dominating set of \(G\) if every vertex not in \(S\) is adjacent with some vertex in \(S\) and the subgraph induced by \(S\) contains a perfect matching.
Włodzimierz Ulatowski
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Paired domination versus domination and packing number in graphs
Journal of Combinatorial Optimization, 2022 14 pages, 8 ...
Magda Dettlaff +2 more
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Unique Minimum Semipaired Dominating Sets in Trees
Discussiones Mathematicae Graph Theory, 2023 Let G be a graph with vertex set V. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two ...
Haynes Teresa W., Henning Michael A.
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs [PDF]
Opuscula Mathematica, 2016 Given a graph \(G=(V,E)\), the subdivision of an edge \(e=uv\in E(G)\) means the substitution of the edge \(e\) by a vertex \(x\) and the new edges \(ux\) and \(xv\).
Magda Dettlaff +2 more
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