Domination polynomial of clique cover product of graphs

Let G be a simple graph of order n. We prove that the domination polynomial of the clique cover product G(C) * H-V(H) is D(G(C) * H, x_ = Pi(k)(i-1)[((1 + x)(ni) - 1)(1 + x)(vertical bar V(H)vertical bar) + D (H, x)], where each clique C-i epsilon C has n(i) vertices. As an application, we study the D-equivalence classes of some families of graphs and, in particular, describe completely the D-equivalence classes of friendship graphs constructed by coalescing n copies of a cycle graph of length 3 with a common vertex.