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Regular orientable embeddings of complete bipartite graphs

✍ Scribed by Jin Ho Kwak; Young Soo Kwon

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 199 KB
Volume: 50
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20097

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✦ Synopsis

Abstract

In this paper, it will be shown that the isomorphism classes of regular orientable embeddings of the complete bipartite graph K~n,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 K~n,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

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