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

作者：Huang, Xueyi; Huang, Qiongxiang^*; Lu, Lu

来源：Algebra Colloquium, 2017, 24(4): 541-550.

DOI：10.1142/S1005386717000359

• Cayley graph
• normal
• automorphism group

Let S-n denote the symmetric group of degree n with n >= 3, S = {c(n) = (1 2 ... n), c(n)(-1), (1 2)} and Gamma(n) = Cay(S-n, S) be the Cayley graph on S-n with respect to S. In this paper, we show that Gamma(n) (n >= 13) is a normal Cayley graph, and that the full automorphism group of Gamma(n) is equal to Aut(Gamma(n)) = R(S-n) (sic) < Inn(phi)> congruent to S-n x Z(2), where R(S-n) is the right regular representation of S-n, phi = (1 2) (3 n) (4 n - 1) (5 n - 2) ... (is an element of S-n), and Inn(phi) is the inner isomorphism of S-n induced by phi.

• 出版日期2017-12
• 单位新疆大学