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Characterizations of trees with equal paired and double domination numbers
Discrete Mathematics, 2006 A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching, and a double dominating set is a dominating set that dominates every vertex of G at least twice.
Mostafa Blidia +2 more
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Distance paired domination numbers of graphs
Discrete Mathematics, 2008 In this paper, we study a generalization of the paired domination number. Let G=(V,E) be a graph without an isolated vertex. A set D⊆V(G) is a k-distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has
Raczek, Joanna
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Upper total domination versus upper paired-domination
Quaestiones Mathematicae, 2007 Let G be a graph with no isolated vertices. A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S, while a paired-dominating set of G is a dominating set of vertices whose induced subgraph has a ...
Paul Dorbec, Michael A Henning
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The Paired Domination Number of Cubic Graphs [PDF]
, 2020 Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γpr(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γpr(G) {\leq} 4n/7 holds for every graph G with δ(
Bin Sheng, Changhong Lü
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Trees With Equal Domination and Paired-Domination Numbers
Ars Comb., 2005 A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G is the minimum cardinality of a paired-dominating set of G, and is obviously bounded below by the ...
Haynes, Teresa W. +2 more
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Twin Paired Domination number of a graph
Journal of Physics: Conference Series, 2020 Abstract A new domination papramter “Twin paired domination number” is introduced in this paper. The set S ⊆ V
G. Mahadevan, M. Vimala Suganthi
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On the domination number of the cartesian product of the path graph and any pair of graphs [PDF]
, 2023 It is known that for any graph $G,$ $γ(G\square P_2)\geq γ(G)$ where $γ$ stands for the domination number, $\square$ for the cartesian product and $P_2$ is the path graph on two vertices. In an attempt to prove Vizing's conjecture, Clark and Suen proved in $2000$ that $γ(X\square Y)\geq \frac{1}{2}γ(X)γ(Y)$ for any pair of graphs $X$ and $Y.$ Combining
Omar Tout
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Paired Disjunctive Domination Number of Middle Graphs [PDF]
CoRRThe concept of domination in graphs plays a central role in understanding structural properties and applications in network theory. In this study, we focus on the paired disjunctive domination number in the context of middle graphs, a transformation that captures both adjacency and incidence relations of the original graph.
Hande Tunçel Gölpek +2 more
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Trees with paired-domination number twice their domination number [PDF]
, 2006 Michael A. Henning +1 more
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