Open Access System for Information Sharing

Login Library

 

Article
Cited 40 time in webofscience Cited 39 time in scopus
Metadata Downloads

REGULAR EMBEDDINGS OF K-N,K-N WHERE N IS A POWER OF 2. I: METACYCLIC CASE SCIE SCOPUS

Title
REGULAR EMBEDDINGS OF K-N,K-N WHERE N IS A POWER OF 2. I: METACYCLIC CASE
Authors
Du, SFJones, GKwak, JHNedela, RSkoviera, M
Date Issued
2007-08
Publisher
ACADEMIC PRESS LTD ELSEVIER SCIENCE L
Abstract
A 2-cell embedding of a graph in an orientable closed surface is called regular if its automorphism group acts regularly on arcs of the embedded graph. The aim of this and of the associated consecutive paper is to give a classification of regular embeddings of complete bipartite graphs K-n.n, where n = 2(e). The method involves groups G which factorize as a product XY of two cyclic groups of order n so that the two cyclic factors are transposed by an involutory automorphism. In particular, we give a classification of such groups G. Employing the classification we investigate automorphisms of these groups, resulting in a classification of regular embeddings of K-n.n, based on that for G. We prove that given n = 2(e) (for e >= 3), there are, up to map isomorphism, exactly 2(e-2) + 4 regular embeddings of K-n.n. Our analysis splits naturally into two cases depending on whether the group G is metacyclic or not. (C) 2006 Elsevier Ltd. All rights reserved.
URI
https://oasis.postech.ac.kr/handle/2014.oak/23268
DOI
10.1016/j.ejc.2006.08.012
ISSN
0195-6698
Article Type
Article
Citation
EUROPEAN JOURNAL OF COMBINATORICS, vol. 28, no. 6, page. 1595 - 1609, 2007-08
Files in This Item:
There are no files associated with this item.

qr_code

  • mendeley

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Views & Downloads

Browse