The second largest eigenvalues of some Cayley graphs on alternating groups

Let $A_n$ denote the alternating group of degree $n$ with $n\ge 3$. The alternating group graph $A{G}_n$, extended alternating group graph $EA{G}_n$ and complete alternating group graph $CA{G}_n$ are the Cayley graphs $\mathrm{C}\mathrm{a}\mathrm{y}(A_n,T_1)$, $\mathrm{C}\mathrm{a}\mathrm{y}(A_n,T_2)$ and $\mathrm{C}\mathrm{a}\mathrm{y}(A_n,T_3)$, respectively, where $T_1=\{(1,2,i),(1,i,2)\mid 3\le i\le n\}$, $T_2=\{(1,i,j),(1,j,i)\mid 2\le i<j\le n\}$ and $T_3={(i,j,k),(i,k,j)\mid 1\leq i<j<k\leq n}$. In this paper, we determine the second largest eigenvalues of $A{G}_n$, $EA{G}_n$ and $CA{G}_n$.