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Journal of Combinatorial Optimization

, Volume 22, Issue 1, pp 1–18 | Cite as

Which trees have a differentiating-paired dominating set?

  • Michael A. HenningEmail author
  • John McCoy
Article
  • 70 Downloads

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.

Keywords

Paired-domination Differentiating-paired dominating Trees 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of KwaZulu-NatalPietermaritzburgSouth Africa

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