Doubly Restrained Domination in Graphs

Let G be a connected simple graph. A subset S of V(G) is a dominating set of G if for every v∈V(G)∖S, there exists x∈S such that xv∈E(G). A set S⊆V(G) is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V(G)∖S. A nonempty subset S⊆V(G) is doubly restrained dominating set of G, if S is a dominating set and both 〈S〉 and 〈V(G)∖S〉 have no isolated vertices. The minimum cardinality of a doubly restrained dominating set of G, denoted by γ_rr (G), is called the doubly restrained domination number of G. In this paper, we initiate the study of the concept and give the domination number of some special graphs and the corona of two graphs.