On Symmetric Cayley Graphs of Valency Eleven-Reference-Cited by-同舟云学术

On Symmetric Cayley Graphs of Valency Eleven

Published:2021-05-11 Issue:02 Volume:28 Page:309-318
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Ling Bo¹,Lou Bengong²,Ma Li³,Yu Xue⁴

Affiliation:

1. School of Mathematics and Computer Sciences, Yunnan Minzu University, Kunming 650504, China

2. School of Mathematics and Statistics, Yunnan University, Kunming 650031, China

3. College of Mathematics and Statistics, Qujing Normal University, Qujing, Yunnan 655011, China

4. Department of Mathematics, Henan Institute of Science and Technology, Xinxiang, Henan 453003, China

Abstract

A Cayley graph [Formula: see text] is said to be normal if [Formula: see text] is normal in [Formula: see text]. In this paper, we investigate the normality problem of the connected 11-valent symmetric Cayley graphs [Formula: see text] of finite nonabelian simple groups [Formula: see text], where the vertex stabilizer [Formula: see text] is soluble for [Formula: see text] and [Formula: see text]. We prove that either [Formula: see text] is normal or [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. Further, 11-valent symmetric nonnormal Cayley graphs of [Formula: see text], [Formula: see text] and [Formula: see text] are constructed. This provides some more examples of nonnormal 11-valent symmetric Cayley graphs of finite nonabelian simple groups after the first graph of this kind (of valency 11) was constructed by Fang, Ma and Wang in 2011.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386721000249