On the total outer-connected domination in graphs

O. Favaron (), H. Karami and S. M. Sheikholeslami ()
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O. Favaron: University Paris Sud and CNRS
H. Karami: Azarbaijan Shahid Madani University
S. M. Sheikholeslami: Azarbaijan Shahid Madani University

Journal of Combinatorial Optimization, 2014, vol. 27, issue 3, No 3, 461 pages

Abstract: Abstract A set S of vertices of a graph G is a total outer-connected dominating set if every vertex in V(G) is adjacent to some vertex in S and the subgraph induced by V∖S is connected. The total outer-connected domination number γ toc (G) is the minimum size of such a set. We give some properties and bounds for γ toc in general graphs and in trees. For graphs of order n, diameter 2 and minimum degree at least 3, we show that $\gamma_{toc}(G)\le \frac{2n-2}{3}$ and we determine the extremal graphs.

Keywords: Total outer-connected dominating set; Total outer-connected domination number; Diameter (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9531-6

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