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.
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