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On the Paired-Domination Subdivision Number of Trees [PDF]
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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The paired-domination and the upper paired-domination numbers of graphs [PDF]
Opuscula Mathematica, 2015 In this paper we continue the study of paired-domination in graphs. A paired-dominating set, abbreviated PDS, of a graph \(G\) with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching.
Włodzimierz Ulatowski
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On the Paired-Domination Subdivision Number of a Graph [PDF]
Mathematics, 2021 In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number sdγpr(G) of G.
Guoliang Hao +4 more
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A Note on the Paired-Domination Subdivision Number of Trees [PDF]
Mathematics, 2021 For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star),
Xiaoli Qiang +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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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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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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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 versus domination and packing number in graphs
Journal of Combinatorial Optimization, 2022 14 pages, 8 ...
Dettlaff, Magda +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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