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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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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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Vertices in all minimum paired-dominating sets of block graphs [PDF]
Journal of Combinatorial Optimization, 2011 Let $G=(V,E)$ be a simple graph without isolated vertices. A set $S\subseteq V$ is a paired-dominating set if every vertex in $V-S$ has at least one neighbor in $S$ and the subgraph induced by $S$ contains a perfect matching. In this paper, we present a linear-time algorithm to determine whether a given vertex in a block graph is contained in all its ...
Chen, Lei, Lu, Changhong, Zeng, Zhenbing
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Double-Quantitative Generalized Multi-Granulation Set-Pair Dominance Rough Sets in Incomplete Ordered Information System [PDF]
Symmetry, 2020 Since the rough sets theory based on the double quantification method was proposed, it has attracted wide attention in decision-making. This paper studies the decision-making approach in Incomplete Ordered Information System (IOIS). Firstly, to better extract the effective information in IOIS, combined with the advantages of set-pair dominance relation
Xue, Zhang, Li, Zhao, Sun
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Pairs of Disjoint Dominating Sets and the Minimum Degree of Graphs [PDF]
Graphs and Combinatorics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Löwenstein, Christian +1 more
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Graphs with disjoint dominating and paired-dominating sets
Open Mathematics, 2010 Abstract A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching.
Southey Justin, Henning Michael
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Locating and paired-dominating sets in graphs
Discrete Applied Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
McCoy, John, Henning, Michael A.
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Optimal Locating-Paired-Dominating Sets in King Grids
, 2022 In this paper, we continue the study of locating-paired-dominating set, abbreviated LPDS, in graphs introduced by McCoy and Henning. Given a finite or infinite graph $G=(V,E)$, a set $S\subset V$ is paired-dominating if the induced subgraph $G[S]$ has a perfect matching and every vertex in $V$ is adjacent to a vertex in $S$.
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Vertices contained in all minimum paired-dominating sets of a tree [PDF]
Czechoslovak Mathematical Journal, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Locating–paired-dominating sets in square grids
Discrete Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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