A New Upper Bound for the Laplacian Spectral Radius of Graphs

Let G be a simple connected graph with n vertices.The matrix Q(G)is said the quasi-Laplacian matrix of G,if it is the sum of the diagonal matrix and the adjacency matrix of G.In this paper,we study some properties of the quasi-Laplacian matrices of G,Moreover we obtain new upper bounds of spectral radius of Laplacian matrices of graphs in terms of the vertex number,the edge number,the largest degree,and the smallest degree of G.