Edge pancyclic Cayley graphs on symmetric group

We study the derangement graph Γₙ whose vertex set consists of all permutations of \1,…,n\, where two vertices are adjacent if and only if their corresponding permutations differ at every position. It is well-known that Γₙ is a Cayley graph, Hamiltonian and Hamilton-connected. In this paper, we prove that for n ≥ 4, the derangement graph Γₙ is edge pancyclic. Moreover, we extend this result to two broader classes of Cayley graphs defined on symmetric group.