Vertices in all minimum paired-dominating sets of block graphs

  • Authors:

  • Lei Chen;Changhong Lu;Zhenbing Zeng

  • Affiliations:

  • College of Information Engineering, Shanghai Maritime University, Shanghai, China 201306 and Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China 200062;Department of Mathematics, East China Normal University, Shanghai, China 200241;Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China 200062

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2012

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Abstract

Let G=(V,E) be a simple graph without isolated vertices. A set S驴V is a paired-dominating set if every vertex in V驴S has at least one neighbor in S and the subgraph induced by S contains a perfect matching. In this paper, we present a linear-time algorithm to determine whether a given vertex in a block graph is contained in all its minimum paired-dominating sets.