On the outer-connected domination in graphs

M. H. Akhbari, R. Hasni, O. Favaron (), H. Karami and S. M. Sheikholeslami ()
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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

Journal of Combinatorial Optimization, 2013, vol. 26, issue 1, No 2, 10-18

Abstract: 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.

Keywords: Outer-connected dominating set; Outer-connected domination number; Diameter (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10878-011-9427-x

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