Counting $\gamma$-sets of Cartesian product with complete graphs

Let G = (V, E) be a simple graph. A set S$\subset$V is a dominating set if every vertex in V\S is adjacent to at least one vertex in S. The domination number $\gamma$ is the minimum cardinality of a dominating set in G. A dominating set of G with cardinality $\gamma$ is called $\gamma$-set of G. In this paper, we count the number of $\gamma$-sets of Cartesian product of G with complete graphs