Optimal orientations of subgraphs of complete bipartite graphs

Abstract

For a graph G, let D(G) be the set of all strong orientations of G. The orientation number of G is min {d(D) |D belongs to D(G)}, where d(D) denotes the diameter of the digraph D. In this paper, we determine the orientation number for some subgraphs of complete bipartite graphs.

Keywords

• subgraphs of complete bipartite graphs
• orientation; orientation number
• $Z_2^n$-partition
• $Z_2^n$-set