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A characterization of graphs with disjoint dominating and paired-dominating sets

Author

Listed:
  • Justin Southey

    (University of KwaZulu-Natal)

  • Michael A. Henning

    (University of KwaZulu-Natal)

Abstract

A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set and the subgraph induced by the set contains a perfect matching. In this paper, we provide a constructive characterization of graphs whose vertex set can be partitioned into a dominating set and a paired-dominating set.

Suggested Citation

  • Justin Southey & Michael A. Henning, 2011. "A characterization of graphs with disjoint dominating and paired-dominating sets," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 217-234, August.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:2:d:10.1007_s10878-009-9274-1
    DOI: 10.1007/s10878-009-9274-1
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    References listed on IDEAS

    as
    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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