ContributionsOn optimal orientations of cartesian products of graphs (I)

For a graph G, let D(G) be the family of strong orientations of G, and define ovbar|d] (G) = mind(D) vb D ] D(G), where d(D) denotes the diameter of the digraph D. Let G × H denote the cartesian product of the graphs G and H. In this paper, we determine completely the values of and , except , where K_n, P_n and C_n denote the complete graph, path and cycle of order n, respectively.