Let G = (V, E) be a simple connected graph of order n ≥ 2, size m with normalized Laplacian eigenvalues ₁ ₂ ₍-₁ > ₙ = 0. Denote with s_ (G) = ₈=₁^n-1 ᵢ^, where α is an arbitrary real number, the sum of powers of normalized Laplacian eigenvalues of graphs. In this paper several inequalities involving invariants of the form sα (G), for various real α are proved. Our results not only generalize and improve some previous results on sα (G), Kemeny constant and Laplacian incidence energy, but also present new bounds for these graph invariants.
Matejic et al. (Wed,) studied this question.