On the bounds for the largest Laplacian eigenvalues of weighted graphs

Abstract

We consider weighted graphs, such as graphs where the edge weights are positive definite matrices. The Laplacian eigenvalues of a graph are the eigenvalues of the Laplacian matrix of a graph G. We obtain an upper bound for the largest Laplacian eigenvalue and we compare this bound with previously known bounds. (C) 2012 Elsevier B.V. All rights reserved.