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Well paired-dominated graphs

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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.

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Authors and Affiliations

  1. University of Prince Edward Island, Charlottetown, PE, Canada, C1A 4P3

    S. L. Fitzpatrick

  2. Saint Mary’s University, Halifax, NS, Canada, B3H 3C3

    B. L. Hartnell

Authors
  1. S. L. Fitzpatrick
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  2. B. L. Hartnell
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Correspondence to S. L. Fitzpatrick.

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Fitzpatrick, S.L., Hartnell, B.L. Well paired-dominated graphs. J Comb Optim 20, 194–204 (2010). https://doi.org/10.1007/s10878-008-9203-8

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  • DOI: https://doi.org/10.1007/s10878-008-9203-8

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