Which trees have a differentiating-paired dominating set?

Michael A. Henning () and John McCoy
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Michael A. Henning: University of KwaZulu-Natal
John McCoy: University of KwaZulu-Natal

Journal of Combinatorial Optimization, 2011, vol. 22, issue 1, No 1, 18 pages

Abstract: Abstract In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998), 199–206). A paired-dominating set of a graph G with no isolated vertex is a dominating set S of vertices whose induced subgraph has a perfect matching. The set S is called a differentiating-paired dominating set if for every pair of distinct vertices u and v in V(G), N[u]∩S≠N[v]∩S, where N[u] denotes the set consisting of u and all vertices adjacent to u. In this paper, we provide a constructive characterization of trees that do not have a differentiating-paired dominating set.

Keywords: Paired-domination; Differentiating-paired dominating; Trees (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10878-009-9268-z

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