On optimal orientations of cartesian products of graphs (I) Original Research Article

For a graph G, let image(G) be the family of strong orientations of G, and define image, 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 image and image, except image, k ⩾ 2, where Kn, Pn and Cn denote the complete graph, path and cycle of order n, respectively.