Automorphism Groups of a Class of Cubic Cayley Graphs on Symmetric Groups

• 来源期刊: 代数集刊（英文版）
• 关键词: Cayley graph normal automorphism group
• 年，卷（期）: 2017,（4）
• 页码范围: 541-550
• 页数: 10页
• 语种: 英文
• DOI: 10.1142/S1005386717000359

摘要

Let Sn denote the symmetric group of degree n with n ≥ 3,S ={cn =(1 2 … n),cn-1,(1 2)} and Tn =Cay(Sn,S) be the Cayley graph on Sn with respect to S.In this paper,we show that Γn (n ≥ 13) is a normal Cayley graph,and that the full automorphism group of Γn is equal to Aut(Γn) =R(Sn) × <Inn(φ)> ≌ Sn x Z2,where R(Sn) is the right regular representation of Sn,φ =(1 2)(3 n)(4 n-1)(5 n-2)… (∈ Sn),and Inn(φ) is the inner isomorphism of Sn induced by φ.