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Well paired-dominated graphs

Author

Listed:
  • S. L. Fitzpatrick

    (University of Prince Edward Island)

  • B. L. Hartnell

    (Saint Mary’s University)

Abstract

A paired-dominating set is a dominating set whose induced subgraph contains at least one perfect matching. This could model the situation of guards or police where each has a partner or backup. We are interested in those where all “minimal” paired-dominating sets are the same cardinality. In this case, we consider “minimal” to be with respect to the pairings. That is, the removal of any two vertices paired under the matching results in a set that is not dominating. We give a structural characterization of all such graphs with girth at least eight.

Suggested Citation

  • S. L. Fitzpatrick & B. L. Hartnell, 2010. "Well paired-dominated graphs," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 194-204, August.
    • Handle: RePEc:spr:jcomop:v:20:y:2010:i:2:d:10.1007_s10878-008-9203-8
    DOI: 10.1007/s10878-008-9203-8
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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.
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