On optimal orientations of cartesian products with a bipartite graph Original Research Article

For a graph G, let D(G) be the family of strong orientations of G. Define d→(G)=min{d(D) | D∈D(G)} and ρ(G)=d→(G)−d(G), where d(D) (resp., d(G)) denotes the diameter of the digraph D (resp., graph G). Let G×H denote the cartesian product of the graphs G and H. In this paper, we show that ρ(G×A1×A2×⋯×Ak)=0, where G is a bipartite graph fulfilling certain weak conditions and {Ai | 1⩽i⩽k} is certain combination of graphs.