Mixed k-rainbow domination numbers in graphs

be an integer. A mixed k-rainbow dominating function (MkRDF) of a graph G = (V;E) is a function f from the set Z = V [ E to the set of all subsets such that for any element z 2 Z with f(z) = ∅ the condition is ful lled, where Nm(z) is the set of all elements either aΣdjacent or incident to the element z. The weight of an MkRDF f is the value !(f) = The mixed k-rainbow domination number of a graph G, denoted by is the minimum weight of an MkRDF of G. In this paper, we initiate the study of the mixed k-rainbow domination number in graphs, and we obtain several bounds for rk(G). In addition, we determine the mixed k-rainbow domination number of some classes of graphs.