2-rainbow domination number of the subdivision of graphs

Let G be a simple graph and f : V (G) -> P ({1, 2}) be a function where for each vertex v is an element of V (G) with f(v) = & empty; we have Uu is an element of NG(v) f(u) = {1, 2}. Then f is a 2-rainbow dominating function (a 2RDF) of G. The weight of f is omega(f) = v is an element of V (G) |f(v)|. The minimum weight among all of 2-rainbow dominating functions is 2-rainbow domination number and is denoted by gamma r2(G). In this paper, we provide some bounds for the 2-rainbow domination number of the subdivision graph S(G) of a graph G. Also, among some other interesting results, we determine the exact value of gamma r2(S(G)) when G is a tree, a bipartite graph, Kr,s, Kn1,n2,...,nk and Kn.