Spectral Condition for a Graph to be Hamiltonian with respect to Normalized Laplacian

FAN Yizheng; YU Guidong

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Spectral Condition for a Graph to be Hamiltonian with respect to Normalized Laplacian

FAN Yizheng 1 *,YU Guidong 2

1.School of Mathematical Sciences, Anhui University, HeFei 230039

2.SchoolofMathematicalSciences,AnhuiUniversity, HeFei 230039

*Correspondence author

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Funding: Specialized Research Fund for the Doctoral Program ofHigher Education （No.20103401110002）, Key Project of Chinese Ministry of Education（No.210091）, Science and Technological Fund ofAnhui Province for Outstanding Youth （No.10040606Y33）, Supported by National Natural ScienceFoundation of China （No.11071002）, NSF of Department of Education of Anhui Province（No.KJ2011A195,KJ2010B136）, Project for Academic Innovation Team of Anhui University （No.KJTD001B）, ScientificResearch Fund for Fostering Distinguished Young Scholars of AnhuiUniversity （No.KJJQ1001）

Opened online:26 March 2012

Accepted by: none

Citation: FAN Yizheng,YU Guidong.Spectral Condition for a Graph to be Hamiltonian with respect to Normalized Laplacian[OL]. [26 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4469947

Let G be a graph and let Δ,δ be the maximum and minimum degrees of G respectively, where Δ/δ<c<√￣2 and c is a constant. In this paper we establish a sufficient spectral condition for G to be Hamiltonian, that is, the nontrivial eigenvalues of the normalized Laplacian of G are sufficiently close to 1.

Keywords:Graph; Hamiltonian; Normalized Laplacian

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