Restrained domination polynomial in graphs

Let G = (V, E) be a graph of order n and size m. A set S subset of V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V - S. The restrained domination number of G, denoted by gamma(r)(G), is the smallest cardinality of a restrained dominating set of G. Let gamma(r)(G, i) denote the number of restrained dominating sets with cardinality i. Then the restrained domination polynomial(RDP) D-r(G, x) of G is defined as D-r(G, x) = Sigma(n)(i=1)d(r)(G,i)x(i). In this paper we determine the restrained domination polynomial for complete graphs, complete bipartite graphs, paths, cycles and products of K-2 with K-k.