On Lee's conjecture and some results

Lixia Fan; Zhihe Liang

ArticleOriginal scientific text

Title

On Lee's conjecture and some results

Authors ¹, ¹

Affiliations

Department of Mathematics, Hebei Normal University, Shijiazhuang 050016, P.R. China

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 = \prod_{k = 0}^{l - 1} (m + 2 k, m + 2 k + 1)

, and

\prod_{k = 0}^{l - 1} (m + 4 k, m + 4 k + 2) (m + 4 k + 1, m + 4 k + 3)

for any positive integers m and l.

Keywords

ENG

permutation graph, graceful, Lee's conjecture

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Title

On Lee's conjecture and some results

Affiliations

Abstract

Keywords

Bibliography