Sharp upper bounds for the Laplacian spectral radius of graphs (Q474024)

Summary: 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 \(\mu(G)\) 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 \(G\).