Geodesic
Domination Parameters of a Graph and its Complement
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 203-215

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A dominating set in a graph G is a set S of vertices such that every vertex in V (G) S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G. Placing constraints on a dominating set yields different domination parameters, including total, connected, restrained, and clique domination numbers. In this paper, we study relationships among domination parameters of a graph and its complement.
Keywords: domination, complement, total domination, connected domination, clique domination, restrained domination 
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     title = {Domination {Parameters} of a {Graph} and its {Complement}},
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Desormeaux, Wyatt J.; Haynes, Teresa W.; Henning, Michael A. Domination Parameters of a Graph and its Complement. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 203-215. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a16/