eng application/pdf 378621 bytes All rights reserved Keywords:Graph spectrum, energy of graphs, resolvent energy MATCH Communications in Mathematical and in Computer Chemistry 86(3) Zogić, Emir Borovićanin, Bojana Glogić, Edin Milovanović, Igor Milovanović, Emina New Bounds for Some Spectrum-Based Topological Indices of Graphs Abstract: The spectrum-based graph invariant E(G), known as (ordinary) energy of a graph G, is defined by E(G) = ∑|λi|, where λ1 > λ2 > • • • > λn are the eigenvalues of G. Recently introduced resolvent energy of a graph is a type of graph energy based on resolvent matrix and defined by ER(G) = ∑(n − λi)-1. The resolvent Estrada index EEr(G) and resolvent signless Laplacian Estrada index SLEEr(G) are defined by EEr(G) = ∑(1 – λi/(n-1))-1 and SLEEr(G) = ∑(1 -qi/(2n−2))-1, respectively, where q1 > q2 > • • • > qn are signless Laplacian eigenvalues of graph G. Using some classical and recently obtained analytic inequalities we obtain several new lower and upper bounds for these graph invariants and improve some of the existing ones. In addition, some relations between the ordinary graph energy E(G) and the resolvent energy ER(G) are established. info:eu-repo/semantics/article 2021 https://phaidrabg.bg.ac.rs/o:28908 ISSN: 0340-6253