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1-REGULAR CAYLEY GRAPHS OF VALENCY 7

Part of: Graph theory

Published online by Cambridge University Press:  08 March 2013

JING JIAN LI ,
GENG RONG ZHANG  and
BO LING
JING JIAN LI*
Affiliation:
School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650031, PR China College of Mathematics and Information Science, Guangxi University, Nanning 530004, PR China email zgrzaw@gxu.edu.cnbolinggxu@163.com
GENG RONG ZHANG
Affiliation:
College of Mathematics and Information Science, Guangxi University, Nanning 530004, PR China email zgrzaw@gxu.edu.cnbolinggxu@163.com
BO LING
Affiliation:
College of Mathematics and Information Science, Guangxi University, Nanning 530004, PR China email zgrzaw@gxu.edu.cnbolinggxu@163.com
*
✉lijjhx@163.com
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Abstract

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A graph $\mit{\Gamma} $ is called $1$-regular if $ \mathsf{Aut} \mit{\Gamma} $ acts regularly on its arcs. In this paper, a classification of $1$-regular Cayley graphs of valency $7$ is given; in particular, it is proved that there is only one core-free graph up to isomorphism.

Keywords

1-regularCayley graphcore-free

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 479 - 485
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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