Discussiones Mathematicae Graph Theory 29(3) (2009) 481-498
doi: 10.7151/dmgt.1459

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ON LEE'S CONJECTURE AND SOME RESULTS

Lixia Fan and Zhihe Liang

Department of Mathematics, Hebei Normal University
Shijiazhuang 050016, P.R. China
e-mail: zhiheliang@163.com.cn

Abstract

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 = ∏k = 0l-1(m+2k,m+2k+1), and ∏k = 0l-1(m+4k,m+4k+2)(m+4k+1,m+4k+3) for any positive integers m and l.

Keywords: permutation graph; graceful, Lee's conjecture.

2000 Mathematics Subject Classification: 05C78.

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Received 13 November 2007
Revised 21 April 2009
Accepted 4 June 2009