Results 11 to 20 of about 2,114 (233)
Total Domination Versus Paired-Domination in Regular Graphs
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph
Cyman Joanna +4 more
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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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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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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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Paired domination versus domination and packing number in graphs
Journal of Combinatorial Optimization, 2022 14 pages, 8 ...
Magda Dettlaff +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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Journal of New Theory, 2023 In this study, transformation graphs obtained from the concept of the total graph and the result of its paired domination number for some special graph families are discussed.
Hande Tunçel Gölpek
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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 ...
Aleksandra Gorzkowska +3 more
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Equitable and Paired Equitable Domination in Inflated Graphs and Their Complements
Axioms, 2023 Domination plays an indispensable role in graph theory. Various types of domination explore various types of applications. Equal-status people work together and interlace with each other easily.
Narayanan Kumaran +4 more
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs [PDF]
Opuscula Mathematica, 2016 Given a graph \(G=(V,E)\), the subdivision of an edge \(e=uv\in E(G)\) means the substitution of the edge \(e\) by a vertex \(x\) and the new edges \(ux\) and \(xv\).
Magda Dettlaff +2 more
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