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A characterization of trees with equal total domination and paired-domination numbers [PDF]

Australas. J Comb., 2004
Let \(G=(V,E)\) be a graph without isolated vertices. A set \(S\subseteq V\) is a total dominating set if every vertex of \(V\) is adjacent to at least one vertex in \(S\). A total dominating set \(S\subseteq V\) is a paired-dominating set if the induced subgraph \(G[S]\) has at least one perfect matching. The paired-domination number \(\gamma_{pr}(G)\)
Erfang Shan, Liying Kang, Michael A. Henning   +2 more
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A New Characterization of Paired Domination Number of a Graph

2012
Paired domination is a relatively interesting concept introduced by Teresa W. Haynes [9] recently with the following application in mind. If we think of each vertex s ∈ S, as the location of a guard capable of protecting each vertex dominated by S, then for a paired domination the guards location must be selected as adjacent pairs of vertices so that ...
G. Mahadevan, A. Nagarajan, A. Selvam, A. Rajeswari   +3 more
openaire   +1 more source

A note on the upper bound for the paired-domination number of a graph with minimum degree at least two

Networks, 2010
Summary: In this note, we give a counter example to show that the proof of a main result obtained by \textit{T. W. Haynes} and \textit{P. J. Slater} [Networks 32, No.3, 199--206 (1998; Zbl 0997.05074), Theorem 12] is inaccurate. Here, we give a complete proof of the result.
Shenwei Huang, Erfang Shan
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Paired domination subdivision and multisubdivision numbers of graphs

Journal of Combinatorial Mathematics and Combinatorial Computing, 2020
The paired domination subdivision number sdpr(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the paired domination number of G. We prove that the decision problem of the paired domination subdivision number is NP-complete even for bipartite graphs.
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Trees with paired-domination number twice their domination number

2007
Udgivelsesdato ...
Henning, Michael A, Vestergaard, Preben D.   +1 more
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Paired-domination game played on cycles

Discrete Applied Mathematics, 2023
Michael A Henning
exaly  

COMPLEMENTARY INDEPENDENT TWIN PAIRED DOMINATION NUMBER OF A GRAPH

Advances in Mathematics: Scientific Journal, 2020
M. Vimala Suganthi, G. Mahadevan
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Paired-domination of Cartesian products of graphs and rainbow domination

Electronic Notes in Discrete Mathematics, 2005
Boštjan Brešar, Michael A Henning, Douglas F Rall   +2 more
exaly  

DISCOVERING COMPLEMENTARY INDEPENDENT TWIN PAIRED DOMINATION NUMBER FOR SOME PRODUCT RELATED GRAPHS

Advances in Mathematics: Scientific Journal, 2020
G. Mahadevan, M. Vimala Suganthi
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A Characterization of Cubic Graphs with Paired-Domination Number Three-Fifths Their Order

Graphs and Combinatorics, 2010
Wayne Goddard, Michael A Henning
exaly