On Lee's conjecture and some results

S.M. Lee proposed the conjecture: for any n > 1 and any permutation f in S(n), the permutation graph P (Pn, f) is graceful. For any integer n > 1 and permutation f in S(n), we discuss the gracefulness of the permutation graph P (Pn, f) if f = ∏l−1 k=0(m + 2k, m + 2k + 1), and ∏l−1 k=0(m+4k, m+4k +2)(m+4k +1, m+4k +3) for any positive integers m and l.