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Mathematical Problems in Engineering
Volume 2013, Article ID 524162, 9 pages
http://dx.doi.org/10.1155/2013/524162
Research Article

Properties and Applications of the Eigenvector Corresponding to the Laplacian Spectral Radius of a Graph

College of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China

Received 26 November 2012; Revised 26 February 2013; Accepted 26 February 2013

Academic Editor: Yong-Kui Chang

Copyright © 2013 Haizhou Song and Qiufen Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the properties of the eigenvector corresponding to the Laplacian spectral radius of a graph and show some applications. We obtain some results on the Laplacian spectral radius of a graph by grafting and adding edges. We also determine the structure of the maximal Laplacian spectrum tree among trees with vertices and pendant vertices ( , fixed), and the upper bound of the Laplacian spectral radius of some trees.