Regular embeddings of Kn,n where n is a power of 2. II: The non-metacyclic case
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- Title
- Regular embeddings of Kn,n where n is a power of 2. II: The non-metacyclic case
- Authors
- Du, SF; Jones, G; Kwak, JH; Nedela, R; Skoviera, M
- Date Issued
- 2010-10
- Publisher
- ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
- Abstract
- The aim of this paper is to complete a classification of regular orientable embeddings of complete bipartite graphs K(n,n), where n = 2(e). The method involves groups G which factorise as a product G = XY of two cyclic groups of order n such that the two cyclic factors are transposed by an involutory automorphism. In particular, we give a classification of such groups G in the case where G is not metacyclic. We prove that for each n = 2(e), e >= 3, there are up to map isomorphism exactly four regular embeddings of K(n,n), such that the automorphism group G preserving the surface orientation and the bi-partition of vertices is a non-metacyclic group, and that there is one such embedding when n = 4. (C) 2010 Elsevier Ltd. All rights reserved.
- Keywords
- COMPLETE BIPARTITE GRAPHS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/25666
- DOI
- 10.1016/J.EJC.2010.01.009
- ISSN
- 0195-6698
- Article Type
- Article
- Citation
- EUROPEAN JOURNAL OF COMBINATORICS, vol. 31, no. 7, page. 1946 - 1956, 2010-10
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