Table of Contents
International Journal of Combinatorics
Volume 2013 (2013), Article ID 520610, 8 pages
http://dx.doi.org/10.1155/2013/520610
Research Article

Bounds for the Largest Laplacian Eigenvalue of Weighted Graphs

Department of Mathematics, Faculty of Sciences and Arts, Nevşehir University, 50300 Nevşehir, Turkey

Received 29 November 2012; Accepted 14 March 2013

Academic Editor: Jun-Ming Xu

Copyright © 2013 Sezer Sorgun. 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

Let be weighted graphs, as the graphs where the edge weights are positive definite matrices. The Laplacian eigenvalues of a graph are the eigenvalues of Laplacian matrix of a graph . We obtain two upper bounds for the largest Laplacian eigenvalue of weighted graphs and we compare these bounds with previously known bounds.