Well paired-dominated graphs

S. L. Fitzpatrick () and B. L. Hartnell
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S. L. Fitzpatrick: University of Prince Edward Island
B. L. Hartnell: Saint Mary’s University

Journal of Combinatorial Optimization, 2010, vol. 20, issue 2, No 6, 194-204

Abstract: 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.

Keywords: Domination; Paired-domination; Matching (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10878-008-9203-8

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