| Abstract: | In this paper, it will be shown that the isomorphism classes of regular orientable embeddings of the complete bipartite graph Kn,n are in one‐to‐one correspondence with the permutations on n elements satisfying a given criterion, and the isomorphism classes of them are completely classified when n is a product of any two (not necessarily distinct) prime numbers. For other n, a lower bound of the number of those isomorphism classes of Kn,n is obtained. As a result, many new regular orientable embeddings of the complete bipartite graph are constructed giving an answer of Nedela‐?koviera's question raised in 12 . © 2005 Wiley Periodicals, Inc. J Graph Theory |
