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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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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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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 +2 more
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A Note on the Paired-Domination Subdivision Number of Trees
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 +2 more
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On the Paired-Domination Subdivision Number of a Graph
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 +2 more
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Upper bounds on the paired-domination number
Applied Mathematics Letters, 2008 A 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 the subgraph induced by S contains a perfect matching.
Xue-Gang Chen +2 more
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Total and paired domination stability in prisms
Discussiones Mathematicae Graph Theory, 2023 A set $D$ of vertices in an isolate-free graph is a total dominating set if every vertex is adjacent to a vertex in $D$. If the set $D$ has the additional property that the subgraph induced by $D$ contains a perfect matching, then $D$ is a paired ...
Michael A. Henning +7 more
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Networks, 1998 In a graph G = (V, E) if we think of each vertex s as the possible location for a guard capable of protecting each vertex in its closed neighborhood N[s], then domination requires every vertex to be protected.
Haynes, Teresa W., Slater, Peter J.
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Total domination versus paired domination [PDF]
Discussiones Mathematicae Graph Theory, 2011 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.
Schaudt, Oliver
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Paired-domination game played in graphs [PDF]
Communications in Combinatorics and Optimization, 2019 In this paper, we continue the study of the domination game in graphs introduced by Bre{\v{s}}ar, Klav{\v{z}}ar, and Rall [SIAM J. Discrete Math. 24 (2010) 979--991].
T.W. Haynes, Michael A. Henning
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