Classification of nonorientable regular embeddings of complete bipartite graphs
SCIE
SCOPUS
- Title
- Classification of nonorientable regular embeddings of complete bipartite graphs
- Authors
- Kwak, JH; Kwon, YS
- Date Issued
- 2011-07
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- 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,K-n into nonorientable surfaces. Such a regular embedding of K-n,K-n exists only when n is of the form n = 2p(1)(a1) p(2)(a2) ... p(k)(ak) where the p(i) are primes congruent to +/- 1 mod 8. In this case, up to isomorphism the number of those regular embeddings of K-n,K-n is 2(k). (C) 2011 Elsevier Inc. All rights reserved.
- Keywords
- Graph; Surface; Regular embedding; Regular map; N-DIMENSIONAL CUBES; POWER; MAPS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/17505
- DOI
- 10.1016/J.JCTB.2011.03.003
- ISSN
- 0095-8956
- Article Type
- Article
- Citation
- JOURNAL OF COMBINATORIAL THEORY SERIES B, vol. 101, no. 4, page. 191 - 205, 2011-07
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