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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 $f={\prod }_{k=0}^{l-1}(m+2k,m+2k+1)$, and ${\prod }_{k=0}^{l-1}(m+4k,m+4k+2)(m+4k+1,m+4k+3)$ for any positive integers m and l.