A class of Hamiltonian and edge symmetric Cayley graphs on symmetric groups

Let S _n be the symmetric group, g _i ⁺ =(123i), g _i ⁻ =(li32) and M _n ⁺ ={g _i ⁺ ∶4≤i≤n}, then M _n ⁺ is a minimal generating set of S _n, where n≥5. It is proved that Cayley graph Cay (S _n, M _n ⁺ ∩M _n ⁻ ) is Hamiltonian and edge symmetric.