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Journal of Combinatorial Optimization

, Volume 26, Issue 1, pp 10–18 | Cite as

On the outer-connected domination in graphs

  • M. H. Akhbari
  • R. Hasni
  • O. Favaron
  • H. Karami
  • S. M. Sheikholeslami
Article

Abstract

A set S of vertices of a graph G is an outer-connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by VS is connected. The outer-connected domination number \(\widetilde{\gamma}_{c}(G)\) is the minimum size of such a set. We prove that if δ(G)≥2 and diam (G)≤2, then \(\widetilde{\gamma}_{c}(G)\le (n+1)/2\), and we study the behavior of \(\widetilde{\gamma}_{c}(G)\) under an edge addition.

Keywords

Outer-connected dominating set Outer-connected domination number Diameter 

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References

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • M. H. Akhbari
    • 1
  • R. Hasni
    • 1
  • O. Favaron
    • 2
  • H. Karami
    • 3
  • S. M. Sheikholeslami
    • 3
  1. 1.School of Mathematical SciencesUniversity Science of MalaysiaPenangMalaysia
  2. 2.Univ Paris-Sud and CNRS, LRI, UMR 8623OrsayFrance
  3. 3.Department of MathematicsAzarbaijan University of Tarbiat MoallemTabrizIran

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