Distance paired-domination problems on subclasses of chordal graphs

Authors:
Lei Chen;Changhong Lu;Zhenbing Zeng
Affiliations:
Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China;Department of Mathematics, East China Normal University, Shanghai, 200241, China;Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China
Venue:
Theoretical Computer Science
Year:
2009

Citing 6
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Abstract

Let G=(V,E) be a graph without isolated vertices. For a positive integer k, a set S@?V is a k-distance paired-dominating set if each vertex in V-S is within distance k of a vertex in S and the subgraph induced by S contains a perfect matching. In this paper, we present two linear time algorithms to find a minimum cardinality k-distance paired-dominating set in interval graphs and block graphs, which are two subclasses of chordal graphs. In addition, we present a characterization of trees with unique minimum k-distance paired-dominating set.