International Journal of Combinatorics
Volume 2013 (2013), Article ID 125916, 3 pages
http://dx.doi.org/10.1155/2013/125916
Research Article

Finite 1-Regular Cayley Graphs of Valency 5

Jing Jian Li,1,2 Ben Gong Lou,1 and Xiao Jun Zhang2,3

1School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650031, China
2School of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China
3School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 15 November 2012; Revised 11 January 2013; Accepted 28 February 2013

Academic Editor: Cai Heng Li

Copyright © 2013 Jing Jian Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let and . We say is -regular Cayley graph if acts regularly on its arcs. is said to be core-free if is core-free in some . In this paper, we prove that if an -regular Cayley graph of valency is not normal or binormal, then it is the normal cover of one of two core-free ones up to isomorphism. In particular, there are no core-free -regular Cayley graphs of valency .