CLASSIFICATION OF REFLEXIBLE REGULAR EMBEDDINGS AND SELF-PETRIE DUAL REGULAR EMBEDDINGS OF COMPLETE BIPARTITE GRAPHS
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- Title
- CLASSIFICATION OF REFLEXIBLE REGULAR EMBEDDINGS AND SELF-PETRIE DUAL REGULAR EMBEDDINGS OF COMPLETE BIPARTITE GRAPHS
- Authors
- Kwak, JH; Kwon, YS
- Date Issued
- 2008-06-06
- Publisher
- ELSEVIER SCIENCE BV
- Abstract
- In this paper, we classify the reflexible regular orientable embeddings and the self-Petrie dual regular orientable embeddings of complete bipartite graphs. The classification shows that for any natural number n, say n = 2(a) p(1)(a1) p(2)(a2) ... p(k)(ak) (p(1,) p(2,)...,p(k) are distinct odd primes and a(i) > 0 foreach i >= 1), there are t distinct reflexible regular embeddings of the complete bipartite graph K-n,K-n up to isomorphism, where t = 1 if a = 0, t = 2(k) if a = 1, t = 2(k+1) if a = 2, and t = 3 . 2(k+1) if a >= 3. And, there are s distinct self-Petrie dual regular embeddings of K-n,K-n up to isomorphism, where s = 1 if a = 0, s = 2(k) if a = 1, s = 2(k+1) if a = 2, and s = 2(k+2) if a >= 3. (C) 2007 Elsevier B.V. All rights reserved.
- Keywords
- complete bipartite graphs; reflexible regular embedding; exponent group; self-Petrie dual; switch exponent group; MAPS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/22817
- DOI
- 10.1016/j.disc.2007.04.062
- ISSN
- 0012-365X
- Article Type
- Article
- Citation
- DISCRETE MATHEMATICS, vol. 308, no. 11, page. 2156 - 2166, 2008-06-06
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