W.J. Desormeaux, T.W. Haynes, M.A. Henning
Domination parameters of a graph and its complement
Discussiones Mathematicae Graph Theory
Received 02.06.2016, Revised 02.11.2016, Accepted 02.11.2016, doi: 10.7151/dmgt.2002
A dominating set in a graph G is a set S of vertices such that every vertex in V(G) \setminus 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.
domination, complement, total domination, connected domination, clique domination, restrained domination