Automorphism groups of a class of cubic Cayley graphs on symmetric groups

2016/09/17 by Xueyi Huang, Qiongxiang Huang, Huang, Xueyi +3 · 1 citation
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1609.05348

Abstract

Let S_n denote the symmetric group of degree n with n≥ 3. Set S=\c_n=(1 2… n),c_n^-1,(1 2)\. Let Γ_n=Cay(S_n,S) be the Cayley graph on S_n with respect to S. In this paper, we show that Γ_n (n≥ 13) is a normal Cayley graph, and that the full automorphism group of Γ_n is equal to Aut(Γ_n)=R(S_n)\rtimes \langleInn(ϕ)⟩≅ S_n\rtimes ℤ₂, where R(S_n) is the right regular representation of S_n, ϕ=(1 2)(3 n)(4 n-1)(5 n-2)⋯ (∈ S_n), and Inn(ϕ) is the inner isomorphism of S_n induced by ϕ.

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• Automorphism Groups and Structure of 4-Valent Cayley Graphs on Dihedral Groups

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