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Graphs and Combinatorics, 2022 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).
Aleksandra Gorzkowska +3 more
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Upper paired domination versus upper domination [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A paired dominating set $P$ is a dominating set with the additional property that $P$ has a perfect matching. While the maximum cardainality of a minimal dominating set in a graph $G$ is called the upper domination number of $G$, denoted by $\Gamma(G ...
Hadi Alizadeh, Didem Gözüpek
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Paired domination stability in graphs
Ars Mathematica Contemporanea, 2021 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).
Aleksandra Gorzkowska +3 more
semanticscholar +4 more sources
On Paired Domination of Some Graphs
Journal of Computational Mathematica, 2022 For a graph a subset D of the vertex set is called a dominating set if every vertex in is adjacent to some vertex in D. The domination number is the minimum cardinality of a dominating set of a graph G.
Rakhimol V. Isaac, Parashree Pandya
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Upper paired domination in graphs
AIMS Mathematics, 2021 A set $ PD\subseteq V(G) $ in a graph $ G $ is a paired dominating set if every vertex $ v\notin PD $ is adjacent to a vertex in $ PD $ and the subgraph induced by $ PD $ contains a perfect matching.
Huiqin Jiang +3 more
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Parameterized Complexity of Paired Domination
International Workshop on Combinatorial AlgorithmsThe 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 matching. In the Paired Domination problem, given a graph G and a positive integer k, the task is to
N. Andreev +5 more
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Paired-Domination Game Played in Graphs
Communications in Combinatorics and Optimization, 2019 Summary: In this paper, we continue the study of the domination game in graphs introduced by \textit{B. Brešar} et al. [SIAM J. Discrete Math. 24, No. 3, 979--991 (2010; Zbl 1223.05189)]. We study the paired-domination version of the domination game which adds a matching dimension to the game.
T. Haynes, Michael A. Henning
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Journal of new theory, 2023 In this study, transformation graphs obtained from the concept of the total graph and the result of its paired domination number for some special graph families are discussed.
Hande Tunçel Gölpek
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Discussiones Mathematicae Graph Theory, 1998 It is known that a dominating set \(S\) of vertices of a graph \(G\) is a set such that every vertex of \(G\) is either in \(S\) or adjacent to at least one member of \(S\). A paired-dominating set is a dominating set whose induced subgraph contains at least one perfect matching.
Fitzpatrick, S., Hartnell, B.
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On the Paired-Domination Subdivision Number of Trees
Mathematics, 2021 A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γpr(G) of G.
Shouliu Wei +4 more
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