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.
Cao et al. (Mon,) studied this question.