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On the outer-connected domination in graphs

Author

Listed:
  • M. H. Akhbari

    (University Science of Malaysia)

  • R. Hasni

    (University Science of Malaysia)

  • O. Favaron

    (Univ Paris-Sud and CNRS, LRI, UMR 8623)

  • H. Karami

    (Azarbaijan University of Tarbiat Moallem)

  • S. M. Sheikholeslami

    (Azarbaijan University of Tarbiat Moallem)

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 V∖S 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.

Suggested Citation

  • M. H. Akhbari & R. Hasni & O. Favaron & H. Karami & S. M. Sheikholeslami, 2013. "On the outer-connected domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 10-18, July.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9427-x
    DOI: 10.1007/s10878-011-9427-x
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    Cited by:

    1. Xiaozhi Wang & Xianyue Li & Bo Hou & Wen Liu & Lidong Wu & Suogang Gao, 2021. "A greedy algorithm for the fault-tolerant outer-connected dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 118-127, January.
    2. D. Pradhan, 2016. "On the complexity of the minimum outer-connected dominating set problem in graphs," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 1-12, January.
    3. Tian Liu & Zhao Lu & Ke Xu, 2015. "Tractable connected domination for restricted bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 247-256, January.

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