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    Some observations on the Laplacian–energy–like invariant of trees
    (Shahin Digital Publisher, 2023) Matejić, Marjan; Milovanović, Igor; Milovanović, Emina; Bozkurt Altındaǧ, Şerife Burcu
    Let G be a graph of order n. Denote by A the adjacency matrix of G and by D = diag(d1, …, dn) the diagonal matrix of vertex degrees of G. The Laplacian matrix of G is defined as L = D − A. Let µ1, µ2, · · ·, µn−1, µn be eigenvalues of L satisfying (formula presented). The Laplacian-energy–like invariant is a graph invariant defined as (formula presented). Improved upper bounds for LEL(G) are obtained and compared when G has a tree structure. © 2022 the authors.