Laplacian-like energy of trees

Abstract

A few alternative definitions of (molecular) graph energy have recently appeared in the literature, among others the Laplacian energy-like invariant, or Laplacian-like energy, defined by Liu and Liu. It was already shown that the Laplacian-like energy shares a number of properties with the usual graph energy. Here we exhibit further similarities between them by showing that among the n-vertex trees, n 6 N, the star Sn has minimal Laplacian-like energy and the path Pn has maximal Laplacian-like energy.