Automorphism group of the complete alternating group graph

الأصل · EN

Let Sₙ and Aₙ denote the symmetric group and alternating group of degree n with n≥ 3, respectively. Let S be the set of all 3-cycles in Sₙ. The complete alternating group graph, denoted by CAGₙ, is defined as the Cayley graph Cay(Aₙ,S) on Aₙ with respect to S. In this paper, we show that CAGₙ (n≥ 4) is not a normal Cayley graph. Furthermore, the automorphism group of CAGₙ for n≥ 5 is obtained, which equals to Aut(CAGₙ)=(R(Aₙ) Inn(Sₙ)) Z₂ (Aₙ Sₙ) Z₂, where R(Aₙ) is the right regular representation of Aₙ, Inn(Sₙ) is the inner automorphism group of Sₙ, and Z₂= h, where h is the map αα⁻¹ (∀ α∈ Aₙ).