In this paper, we continue the study of paired domination in graphs introduced by Haynes and Slater [T.W. Haynes, P.J. Slater, Paired-domination in graphs, ...
An upper bound on the paired-domination number in terms ...
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An upper bound on the paired-domination number in terms of the number of edges in the graph · Michael A. Henning · Published in Discrete Mathematics 1 November ...
The paired-domination number of a graph G, denoted by γpr(G), is the minimum cardinality of a paired-dominating set in G. We show that if G is a connected graph ...
First, we present an upper bound on the paired-domination number of a graph with girth at least 6 in terms of its minimum degree. Lemma 1. Hall [6].
A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and the subgraph induced by S contains ...
Feb 11, 2011 · To simplify the notation, we shall write PDS to mean “paired-dominating set”. Moreover, given a graph G = (V(G),E(G)), we denote by G[S] the ...
Jun 30, 2024 · Having an upper bound in terms of the number of edges of G G is useful when dealing with classes of graphs whose number of edges directly ...
The following result provides an upper bound on the paired-domination number of a graph with minimum degree at least 2 and girth at least 6 in terms of its ...
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Our purpose in this paper is to establish the above upper bound on the paired-domination number for trees. We make use of the following results in this ...