Regular embeddings of complete multipartite graphs

Authors:
Shao-Fei Du;Jin Ho Kwak;Roman Nedela
Affiliations:
Mathematics, Capital Normal University, Beijing 100037, China;Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea;Institute of Mathematics, Slovak Academy of Sciences, Banská Bystrica, Slovakia
Venue:
European Journal of Combinatorics - Special issue: Topological graph theory II
Year:
2005

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Abstract

In this paper, we classify all regular embeddings of the complete multipartite graphs Kp,...,p for a prime p into orientable surfaces. Also, the same work is done for the regular embeddings of the lexicographical product of any connected arc-transitive graph of prime order q with the complement of the complete graph of prime order p, where q and p are not necessarily distinct. Lots of regular maps found in this paper are Cayley maps.