Rainbow domination number in graphs

A k-rainbow domination function of a graph Gis a function f that assigns to each vertex a set of colorschosen from the set {1, 2, ..., k}, such that for any vertexvϵ V (G), f(v) = f(v)=ø implies U(uϵ)N(v) f(u) = {1, 2,..., k}. Thek-rainbow domination number γrk(G) of a graph G is theminimum ω(f) = Σ(vϵV(G). |f(v)| over all such functions f.In this note we study 2-rainbow domination parameters ingraphs.