Complete bipartite graphs with a unique regular embedding

Authors:
Gareth Jones;Roman Nedela;Martin Škoviera
Affiliations:
School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom;Mathematical Institute of Slovak Academy of Sciences, Matej Bel University, 975 49 Banská Bystrica, Slovakia;Department of Informatics, Comenius University, 842 48 Bratislava, Slovakia
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

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Abstract

We show that the complete bipartite graph K"n","n has a unique regular embedding in an orientable surface if and only if n is coprime to @f(n). The method, involving groups which factorise as a product of two cyclic groups, is also used to classify such embeddings when n is the square of a prime.