Labelling algorithms for paired-domination problems in block and interval graphs

Lei Chen, Changhong Lu () and Zhenbing Zeng
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Lei Chen: East China Normal University
Changhong Lu: East China Normal University
Zhenbing Zeng: East China Normal University

Journal of Combinatorial Optimization, 2010, vol. 19, issue 4, No 2, 457-470

Abstract: Abstract Let G=(V,E) be a graph without isolated vertices. A set S⊆V is a paired-dominating set if every vertex in V−S is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination problem is to determine the paired-domination number, which is the minimum cardinality of a paired-dominating set. Motivated by a mistaken algorithm given by Chen, Kang and Ng (Discrete Appl. Math. 155:2077–2086, 2007), we present two linear time algorithms to find a minimum cardinality paired-dominating set in block and interval graphs. In addition, we prove that paired-domination problem is NP-complete for bipartite graphs, chordal graphs, even for split graphs.

Keywords: Algorithm; Block graph; Interval graph; Paired-domination; NP-complete (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10878-008-9177-6

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