Regular embeddings of Kn,n where n is a power of 2. I: Metacyclic case
European Journal of Combinatorics
Classification of regular embeddings of n-dimensional cubes
Journal of Algebraic Combinatorics: An International Journal
Classification of nonorientable regular embeddings of complete bipartite graphs
Journal of Combinatorial Theory Series B
On the orientable regular embeddings of complete multipartite graphs
European Journal of Combinatorics
A classification of orientably-regular embeddings of complete multipartite graphs
European Journal of Combinatorics
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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-Škoviera's question raised in [12]. © 2005 Wiley Periodicals, Inc. J Graph Theory