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Title: Paired-domination in inflated graphs
Authors: Kang, Liying
Sohn, Moo Young
Cheng, T. C. Edwin
Subjects: Domination
Inflated graphs
Perfect matching
Issue Date: Jun-2004
Publisher: Elsevier B.V.
Source: Theoretical computer science, June 2004, v. 320, no. 2-3, p. 485-494.
Abstract: The inflation G[sub I] of a graph G with n(G) vertices and m(G) edges is obtained from G by replacing every vertex of degree d of G by a clique K[sub d]. 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 if the subgraph induced by S contains a perfect matching. The paired domination number γ[sub p](G) is the minimum cardinality of a paired dominating set of G. In this paper, we show that if a graph G has a minimum degree δ(G)≥2, then n(G)≤γ[sub p](GI)≤4m(G)/[δ(G)+1], and the equality γ[sub p](GI)=n(G) holds if and only if G has a perfect matching. In addition, we present a linear time algorithm to compute a minimum paired-dominating set for an inflation tree.
Rights: Theoretical Computer Science © 2004 Elsevier B.V. The journal web site is located at
Type: Journal/Magazine Article
DOI: 10.1016/j.tcs.2004.02.028
ISSN: 0304-3975
Appears in Collections:LMS Journal/Magazine Articles

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