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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 $\Gamma(G)$, the maximum cardinality of a minimal paired dominating set in $G$ is called the upper paired ...
Alizadeh, Hadi, Gözüpek, Didem
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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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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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Minimal graphs with disjoint dominating and paired-dominating sets
Discussiones Mathematicae Graph Theory, 2021 A subset $D\subseteq V_G$ is a dominating set of $G$ if every vertex in $V_G-D$ 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. A graph $G$ is a $D\!P\!D\!P$-graph if it has a pair $(D,P)$ of disjoint sets of vertices of $G$ such that $D$ is a ...
Henning Michael A., Topp Jerzy
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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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Total domination versus paired domination [PDF]
Discussiones Mathematicae Graph Theory, 2012 A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by t.
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Total domination versus paired-domination in regular graphs
Discussiones Mathematicae Graph Theory, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cyman Joanna +4 more
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European Journal of Combinatorics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Balister, Paul, Bollobás, Béla
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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 ...
Gorzkowska, Aleksandra +3 more
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Disjoint Paired-Dominating sets in Cubic Graphs [PDF]
Graphs and Combinatorics, 2019 A paired-dominating set of a graph G is a dominating set D with the additional requirement that the induced subgraph G[D] contains a perfect matching. We prove that the vertex set of every claw-free cubic graph can be partitioned into two paired-dominating sets.
Gábor Bacsó +3 more
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