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Author Kwak, Jin Ho ♦ Kwon, Young Soo
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2010-01-17
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Combinatorics ♦ 05C10 ♦ 05C30 ♦ math
Abstract A 2-cell embedding of a graph $G$ into a closed (orientable or nonorientable) surface is called regular if its automorphism group acts regularly on the flags - mutually incident vertex-edge-face triples. In this paper, we classify the regular embeddings of complete bipartite graphs $K_{n,n}$ into nonorientable surfaces. Such regular embedding of $K_{n,n}$ exists only when $n = 2p_1^{a_1}p_2^{a_2}... p_k^{a_k}$ (a prime decomposition of $n$) and all $p_i \equiv \pm 1 (\mod 8)$. In this case, the number of those regular embeddings of $K_{n,n}$ up to isomorphism is $2^k$.
Educational Use Research
Learning Resource Type Article


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