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Paired-domination in subdivided star-free graphs
Graphs and Combinatorics, 2010 International audienceA 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 in S and if the subgraph induced by S contains a perfect matching.
Dorbec, Paul, Gravier, Sylvain
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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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Graphs and Combinatorics, 2022 AbstractA 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 paired domination number, $$\gamma _{\mathrm{pr}}(G)$$ γ
Aleksandra Gorzkowska +3 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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Complexity of Paired Domination in AT-free and Planar Graphs [PDF]
SSRN Electronic Journal, 2022 For 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), if $G[D]$, the subgraph induced by $D$ in $G$ has a perfect matching. The Min-PD problem requires
Vikash Tripathi +4 more
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Paired domination stability in graphs
Ars Mathematica Contemporanea, 2022 Summary: 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 paired domination number, \(\gamma_{\mathrm{pr}} (G)\), of \(G\) is the minimum cardinality of a paired ...
Aleksandra Gorzkowska +3 more
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Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets
Discussiones Mathematicae Graph Theory, 2021 A subset D ⊆ VG is a dominating set of G if every vertex in VG – D has a neighbor in D, while D is a paired-dominating set of G if D is a dominating set and the subgraph induced by D contains a perfect matching.
Henning Michael A., Topp Jerzy
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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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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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Equitable and Paired Equitable Domination in Inflated Graphs and Their Complements
Axioms, 2023 Domination plays an indispensable role in graph theory. Various types of domination explore various types of applications. Equal-status people work together and interlace with each other easily.
Narayanan Kumaran +4 more
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