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Inequalities of Nordhaus-Gaddum type for doubly connected domination number |
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| Authors: | M.H. Akhbari O. Favaron |
| Affiliation: | a School of Mathematical Sciences, University Science of Malaysia, 11800 Penang, Malaysia b Univ Paris-Sud and CNRS, LRI, UMR 8623, Orsay, F-91405, France c Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R., Iran |
| Abstract: | A set S of vertices of a connected graph G is a doubly connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraphs induced by S and V−S are connected. The doubly connected domination numberγcc(G) is the minimum size of such a set. We prove that when G and  are both connected of order n,  and we describe the two infinite families of extremal graphs achieving the bound. |
| Keywords: | Doubly connected dominating set Doubly connected domination number Nordhaus-Gaddum inequalities |
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