The first to ninth greatest LEL-invariants of connected graphs

Abstract

Let G be a connected graph with n vertices, and μ₁, μ₂,..., μ_n be the Laplacian eigenvalues of G. The Laplacian-energy-like invariant (short for LEL-invariant) of a graph, denoted as LEL(G) =Σⁿ_i=1√μ_i, has been defined and investigated in [J. Liu, B. Liu, A Laplacian-energy-like invariant of a graph, MATCH Commun. Math. Comput. Chem., 59 (2008), 355-372]. In this paper, the first to ninth greatest LEL-invariants, together with the corresponding graphs among the class of connected n-vertex graphs are determined.