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

Abstract

Let Sndenote the symmetric group of degree n with n ≥ 3, S = { cn= (1 2 ⋯ n), [Formula: see text], (1 2)} and Γn= Cay(Sn, S) be the Cayley graph on Snwith respect to S. In this paper, we show that Γn(n ≥ 13) is a normal Cayley graph, and that the full automorphism group of Γnis equal to Aut(Γn) = R(Sn) ⋊ 〈Inn(ϕ) ≅ Sn× 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 Sninduced by ϕ.