LAUSR

Let $$A_n$$An denote the alternating group of degree n with $$n\ge 3$$n≥3. The alternating group graph $$AG_n$$AGn, extended alternating group graph $$EAG_n$$EAGn and complete alternating group graph $$CAG_n$$CAGn are the Cayley graphs $$\mathrm {Cay}(A_n,T_1)$$Cay(An,T1), $$\mathrm {Cay}(A_n,T_2)$$Cay(An,T2) and $$\mathrm {Cay}(A_n,T_3)$$Cay(An,T3), respectively, where $$T_1=\{(1,2,i),(1,i,2)\mid 3\le i\le n\}$$T1={(1,2,i),(1,i,2)∣3≤i≤n}, $$T_2=\{(1,i,j),(1,j,i)\mid 2\le i