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Vertices in all minimum paired-dominating sets of block graphs

Author

Listed:
  • Lei Chen

    (Shanghai Maritime University
    East China Normal University)

  • Changhong Lu

    (East China Normal University)

  • Zhenbing Zeng

    (East China Normal University)

Abstract

Let G=(V,E) be a simple graph without isolated vertices. A set S⊆V is a paired-dominating set if every vertex in V−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.

Suggested Citation

  • Lei Chen & Changhong Lu & Zhenbing Zeng, 2012. "Vertices in all minimum paired-dominating sets of block graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 176-191, October.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9375-5
    DOI: 10.1007/s10878-011-9375-5
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    References listed on IDEAS

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    1. Michael A. Henning, 2007. "Graphs with large paired-domination number," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 61-78, January.
    2. Paul Dorbec & Sylvain Gravier & Michael A. Henning, 2007. "Paired-domination in generalized claw-free graphs," Journal of Combinatorial Optimization, Springer, vol. 14(1), pages 1-7, July.
    3. Michael A. Henning & Michael D. Plummer, 2005. "Vertices Contained in all or in no Minimum Paired-Dominating Set of a Tree," Journal of Combinatorial Optimization, Springer, vol. 10(3), pages 283-294, November.
    Full references (including those not matched with items on IDEAS)

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