Let G=(V,E) be a graph with the vertex set V=V(G) and the edge set E=E(G). Let k be a positive integer, [k]={1,2,…,k} and 𝒫([k]) be the power set of [k]. A function f:V(G)→𝒫([k]) is a k-rainbow dominating function if for every vertex x with f(x)=𝜙, f(N(x))=[k]. The k-rainbow domination number 𝛾rk(G) is the minimum weight of Σ|𝑓(𝑥)| 𝑥ε 𝑉(𝐺)taken over all k-rainbow functions. We investigate the rainbow domination and independent rainbow domination numbers of classes of graphs.
