Given a graph G and a natural number k, the k graph product of G = (V,E) is the graph with vertex set V . For every two vertices x = (x1, . . . , xk) and y = (y1, . . . , yk) in V , an edge is placed according to a predefined rule. Graph products are a basic combinatorial object, widely studied and used in different areas such as hardness of approximation, information theory, etc. We study grap...