Ordering Trees with n vertices and diameter d by their largest Laplacian eigenvalues

Abstract

The set of trees with n vertices and diameter d is denoted by T _n,d. In this paper, we give the first [d/2] trees in T_n,d ordered according to their largest Laplacian eigenvalues in decreasing order, and determine all trees in T_n,d whose largest Laplacian eigenvalue is greater than n - d + 1.