\(1\)-regular Cayley graphs of valency \(7\)

Authors

  • J. J. Li College of Mathematics and Information Science, Guangxi University, Nanning, 530004, P. R. China.
  • G. R. Zhang College of Mathematics and Information Science, Guangxi Univer- sity, Nanning, 530004, P. R. China
  • B. Ling College of Mathematics and Information Science, Guangxi Univer- sity, Nanning, 530004, P. R. China

Keywords:

$1$-regular, Cayley graph, core-free

Abstract

A graph $\Ga$ is called $1$-regular if $\Aut(\Ga)$ acts regularly on its arcs. In this paper, we give a complete classification or characterization of $1$-regular Cayley graphs valency $7$. We prove that a $1$-regular Cayley graph of valency $7$ is either normal or bi-normal, or is a normal cover of a core-free one(up to isomorphic). As far as we known the result for the classification of 1-regular graphs is scarcely. 10.1017/S0004972713000087

Published

2013-09-27

Issue

Vol. 88 No. 3 (2013)

Section

Articles
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