Ordering trees by their Laplacian spectral radii

Denote by Tn the set of trees on n vertices. Zhang, Li [X.D. Zang, J.S. Li, The two largest eigenvalues of Laplacian matrices of trees (in Chinese), J. China Univ. Sci. Technol. 28 (1998) 513-518] and Guo [J.M. Guo, On the Laplacian spectral radius of a tree, Linear Algebra Appl. 368 (2003) 379-385] give the first four trees in Tn, ordered according to their Laplacian spectral radii. In this paper, we determine the fifth to eighth trees in the above ordering.