On locally primitive Cayley graphs of finite simple groups

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Fang, Xingui^1,2  Ma, Xuesong³  Wang, Jie^1,2 

[1] Peking Univ, LMAM, Beijing 100871, Peoples R China

[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[3] Capital Normal Univ, Dept Math, Beijing 100048, Peoples R China

关键词: Finite simple group;    Maximal subgroup;    Cayley graph;    Normal Cayley graph;    Arc-transitive graph;    Locally primitive graph;   

DOI  :  10.1016/j.jcta.2010.10.008

来源: Elsevier

【 摘 要 】

In this paper we investigate locally primitive Cayley graphs of finite nonabelian simple groups. First, we prove that, for any valency d for which the Weiss conjecture holds (for example, d <= 20 or d is a prime number by Conder, Li and Praeger (2000) [1]), there exists a finite list of groups such that if G is a finite nonabelian simple group not in this list, then every locally primitive Cayley graph of valency d on G is normal. Next we construct an infinite family of p-valent non-normal locally primitive Cayley graph of the alternating group for all prime p >= 5. Finally, we consider locally primitive Cayley graphs of finite simple groups with valency 5 and determine all possible candidates of finite nonabelian simple groups G such that the Cayley graph Cay(G, S) might be non-normal. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free