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.
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Research of S.M. Sheikholeslami was supported by the Research Office of Azarbaijan University of Tarbiat Moallem.
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Akhbari, M.H., Hasni, R., Favaron, O. et al. On the outer-connected domination in graphs. J Comb Optim 26, 10–18 (2013). https://doi.org/10.1007/s10878-011-9427-x
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DOI: https://doi.org/10.1007/s10878-011-9427-x