Sharp Upper Bounds for the Laplacian Spectral Radius of Graphs

الملخص EN

The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power network to distributed control of formations.

Let G=(V,E) be a simple connected graph on n vertices and let μ(G) be the largest Laplacian eigenvalue (i.e., the spectral radius) of G.

In this paper, by using the Cauchy-Schwarz inequality, we show that the upper bounds for the Laplacian spectral radius of G.