Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/629
Title: | Paired-domination in inflated graphs | Authors: | Kang, L Sohn, MY Cheng, TCE |
Issue Date: | Jun-2004 | 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. | Keywords: | Domination Inflated graphs Perfect matching |
Publisher: | Elsevier | Journal: | Theoretical computer science | ISSN: | 0304-3975 | DOI: | 10.1016/j.tcs.2004.02.028 | Rights: | Theoretical Computer Science © 2004 Elsevier B.V. The journal web site is located at http://www.sciencedirect.com. |
Appears in Collections: | Journal/Magazine Article |
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File | Description | Size | Format | |
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inflatC.pdf | Pre-published version | 178.74 kB | Adobe PDF | View/Open |
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