The second largest eigenvalues of some Cayley graphs on alternating groups

Abstract

Let An denote the alternating group of degree n with n≥ 3. The alternating group graph AGn, extended alternating group graph EAGn and complete alternating group graph CAGn are the Cayley graphs Cay (An, T1) , Cay (An, T2) and Cay (An, T3) , respectively, where T1= { (1 , 2 , i) , (1 , i, 2) ∣ 3 ≤ i≤ n} , T2= { (1 , i, j) , (1 , j, i) ∣ 2 ≤ i< j≤ n} and T3= { (i, j, k) , (i, k, j) ∣ 1 ≤ i< j< k≤ n}. In this paper, we determine the second largest eigenvalues of AGn, EAGn and CAGn.