Automorphism groups of a family of Cayley graphs of the alternating groups

Let A(n) be the alternating group of degree n with n >= 5. Set S = {(1 i j), (1 ji)vertical bar 2 <= i, j <= n, i not equal j}. In this paper, it is shown that the full automorphism group of the Cayley graph Cay(A(n), S) is the semi-product R(A(n)) x Aut(A(n), S), where R(A(n)) is the right regular representation of A(n) and Aut(A(n), S) = {phi is an element of Aut(A(n)) vertical bar S-phi = S}congruent to Sn-1