Which trees have a differentiating-paired dominating set?

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]∩SN[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.

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Correspondence to Michael A. Henning.

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Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.

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Henning, M.A., McCoy, J. Which trees have a differentiating-paired dominating set?. J Comb Optim 22, 1–18 (2011). https://doi.org/10.1007/s10878-009-9268-z

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Keywords

  • Paired-domination
  • Differentiating-paired dominating
  • Trees