info:eu-repo/semantics/article On the Conjecture Related ti the Energy of Graphs with Sefl-Loops MATCH Communications in Mathematical and in Computer Chemistry 89(2) 2023 Abstract: Let Gσ be a graph obtained by attaching a self-loop, or just a loop, for short, at each of σ chosen vertices of a given graph G. Gutman et al. have recently introduced the concept of the energy of graphs with self-loops, and conjectured that the energy E(G) of a graph G of order n is always strictly less than the energy E(Gσ ) of a corresponding graph Gσ , for 1 ≤ σ ≤ n − 1. In this paper, a simple set of graphs which disproves this conjecture is exposed, together with some remarks regarding the standard deviations of the (adjacency) eigenvalues of G and Gσ , respectively. Keywords:Graph energy, topological indices https://phaidrabg.bg.ac.rs/o:28972 doi: 10.46793/match.89-2.479J ISSN: 0340-6253 All rights reserved application/pdf 486118 bytes eng Jovanović, Irena Glogić, Edin Zogić, Emir