Skip to main content
SpringerLink
Log in

Paired-domination of Trees

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

Let G= (V, E) be a graph without isolated vertices. A set S⊂V is a paired-dominating set if it dominates V and the subgraph induced by S,〈S〉, contains a perfect matching. The paired-domination number γp(G) is defined to be the minimum cardinality of a paired-dominating set S in G. In this paper, we present a linear-time algorithm computing the paired-domination number for trees and characterize trees with equal domination and paired-domination numbers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Haynes, T.W. and Slater, P.J. (1998), Paired-domination in graphs. Networks 32, 199–206.

    Google Scholar 

  2. Haynes, T.W., Hedetniemi, S.T. and Slater, P.J. (1998), Fundamentals of Domination in Graphs. Marcel Dekker, New York.

    Google Scholar 

  3. Haynes, T.W., Hedetniemi, S.T. and Slater, P.J. (1998), Domination in Graphs: Advanced Topics. Marcel Dekker, New York.

    Google Scholar 

  4. Hattingh, J.H. and Henning, M.A. (2000), Characterizations of trees with equal domination parameters. Journal of Graph Theory 34, 142–153.

    Google Scholar 

  5. Cockayne, E.J., Favaron, O., Mynhardt, C.M. and Puech, J. (2000), A characterization of (γ, i)-trees. Journal of Graph Theory 34, 277–292.

    Google Scholar 

  6. Mynhardt, C.M. (1999), Vertices contained in every minimum dominating set of a tree. Journal of Graph Theory 31, 163–177.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China

    Hong Qiao

  2. Department of Mathematics, Shanghai University, Shanghai, 200436, 3, China

    Liying Kang

  3. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Mihaela Cardei & Ding-Zhu Du

Authors
  1. Hong Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liying Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mihaela Cardei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ding-Zhu Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qiao, H., Kang, L., Cardei, M. et al. Paired-domination of Trees. Journal of Global Optimization 25, 43–54 (2003). https://doi.org/10.1023/A:1021338214295

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021338214295

Keywords

Search

Navigation