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Upper bounds on the paired-domination number [PDF]
Applied Mathematics Letters, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuegang Chen +2 more
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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.
Schaudt, Oliver
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Total and paired domination stability in prisms [PDF]
Discussiones Mathematicae Graph Theory, 2023 Summary: 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 dominating set of \(G\).
Aleksandra Gorzkowska +3 more
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Block Graphs with Large Paired Domination Multisubdivision Number [PDF]
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
doaj +2 more sources
Paired-domination of Cartesian products of graphs and rainbow domination
Electronic Notes in Discrete Mathematics, 2005 Abstract The most famous open problem involving domination in graphs is Vizing's conjecture which states the domination number of the Cartesian product of any two graphs is at least as large as the product of their domination numbers. We investigate a similar problem for paired-domination, and obtain a lower bound in terms of product of domination ...
Michael Henning +2 more
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Paired-domination in inflated graphs [PDF]
Theoretical Computer Science, 2004 The paper studies inflated graphs of graphs. If \(G\) is a graph, then the inflated graph \(G_I\) of \(G\) is defined. It is obtained from \(G\) by replacing each vertex \(x\) of \(G\) by a clique with the number of vertices equal to the degree of \(x\) in \(G\) and replacing each edge between two vertices by an edge joining vertices of these cliques ...
Liying Kang +2 more
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Perfectly relating the domination, total domination, and paired domination numbers of a graph
Discrete Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dieter Rautenbach, Simone Dantas
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Parameterized Complexity of Paired Domination [PDF]
The Paired Domination problem is one of the well-studied variants of the classical Dominating Set problem. In a graph G on nvertices, a dominating set D (set of vertices such that N[D] = V (G)) is called a paired dominating set of G, if G[D] has perfect matching. In the Paired Domination problem, given a graph G and a positive integer k, the task is to
Andreev, Nikita +5 more
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Distance paired domination numbers of graphs [PDF]
Discrete Mathematics, 2008 Let \(G=(V,E)\) be a graph without an isolated vertex. A set \(D\subset V(G)\) is a dominating set of \(G\) if every vertex in \(V(G)-D\) is adjacent to at least one vertex in \(D\). A set \(D\subset V(G)\) is a paired dominating set of \(G\) if it is dominating and the indiced subgraph \(\) has a perfect matching.
Raczek, Joanna
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Paired-domination in graphs [PDF]
, 2013 D.Phil. (Mathematics) Domination and its variants are now well studied in graph theory. One of these variants, paired-domination, requires that the subgraph induced by the dominating set contains a perfect matching. In this thesis, we further investigate the concept of paired-domination. Chapters 2, 3, 4, and 5 of this thesis have been published in [17]
McCoy, John Patrick
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