Characterizing Trees with Large Laplacian Energy

Eliseu Fritscher; Carlos Hoppen; Israel Rocha; Vilmar Trevisan

doi:10.1016/j.laa.2013.01.028

paper

Characterizing Trees with Large Laplacian Energy

arXiv:1205.6487 · doi:10.1016/j.laa.2013.01.028

Abstract

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 $n$ 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 $k \in {1, ..., n}$ .