On Lee's conjecture

Abstract

S.M.Lee proposed the conjecture: for any n > 1 and any permutation/in S(n), the permutation graph P(P _n,f) is graceful. For any integer n ≥ 5 and some permutations f in S(n), we discuss gracefulness of the permutation graphs P(P _n,f) if f= (m, m + 1, m + 2,m + 3, m + 4), (m,m + 2)(m + 1, m + 3), (m,m + 1, m + 2, m + 4, m + 3), (m, m + 1, m + 4, m + 3, m + 2), (m, m + 2, m + 3, m + 4, m + 1), (m, m + 3, m + 4, m + 2, m + 1) and (m, m + 4, m + 3, m + 2, m + 1).