On the Laplacian spectral radius of a tree

Let G be a graph; its Laplacian matrix is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. In this paper, we present a sharp upper bound for the Laplacian spectral radius of a tree in terms of the matching number and number of vertices, and deduce from that the largest few Laplacian spectral radii over the class of trees on a given number of vertices.