Bounds for the Laplacian spectral radius of graphs

Abstract

This paper is a survey on the upper and lower bounds for the largest eigenvalue of the Laplacian matrix, known as the Laplacian spectral radius, of a graph. The bounds are given as functions of graph parameters like the number of vertices, the number of edges, degree sequence, average 2-degrees, diameter, covering number, domination number, independence number and other parameters.

Keywords

• graph, laplacian matrix, laplacian spectral radius, upper bound, lower bound