Set domination in graphs

Let G = (V, E) be a connected graph. A set D ? V is a set-dominating set (sd-set) if for every set T ? V ? D, there exists a nonempty set S ? D such that the subgraph 〈S ∪ T〉 induced by S ∪ T is connected. The set-domination number γ_s(G) of G is the minimum cardinality of a sd-set. In this paper we develop properties of this new parameter and relate it to some other known domination parameters.