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Vertices Contained in all or in no Minimum Paired-Dominating Set of a Tree

Author

Listed:
  • Michael A. Henning

    (University of KwaZulu-Natal)

  • Michael D. Plummer

    (Vanderbilt University)

Abstract

A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. We characterize the set of vertices of a tree that are contained in all, or in no, minimum paired-dominating sets of the tree.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:10:y:2005:i:3:d:10.1007_s10878-005-4107-3
    DOI: 10.1007/s10878-005-4107-3
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    Citations

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    Cited by:

    1. 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.
    2. Michael A. Henning & John McCoy, 2011. "Which trees have a differentiating-paired dominating set?," Journal of Combinatorial Optimization, Springer, vol. 22(1), pages 1-18, July.
    3. 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.
    4. Michael A. Henning, 2007. "Graphs with large paired-domination number," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 61-78, January.
    5. 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.
    6. Paul Dorbec & Michael A. Henning, 2011. "Upper paired-domination in claw-free graphs," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 235-251, August.

    More about this item

    Keywords

    paired-domination number; tree;

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