Skip to main content

Which trees have a differentiating-paired dominating set?


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.

This is a preview of subscription content, access via your institution.


Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Michael A. Henning.

Additional information

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

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Henning, M.A., McCoy, J. Which trees have a differentiating-paired dominating set?. J Comb Optim 22, 1–18 (2011).

Download citation

  • Published:

  • Issue Date:

  • DOI:


  • Paired-domination
  • Differentiating-paired dominating
  • Trees