Characterizing trees with large Laplacian energy

We investigate the problem of ordering trees according to their Laplacian energy. More precisely, given a positive integer n, we find a class of cardinality approximately root n whose elements are the n-vertex trees with largest Laplacian energy. The main tool for establishing this result is a new upper bound on the sum S-k(T) of the k largest Laplacian eigenvalues of an n-vertex tree T with diameter at least four, where k is an element of [1, .. , n}. (C) 2013 Elsevier Inc. All rights reserved.