On the Conjecture Related to the Energy of Graphs with Self–Loops MATCH Communications in Mathematical and in Computer Chemistry 89(2) Jovanović, Irena M. Zogić, Emir Glogić, Edin Keywords: Graph spectrum, energy of graphs, energy of graphs with self-loops All rights reserved application/pdf 486118 bytes eng https://phaidrabg.bg.ac.rs/o:28906 doi:10.46793/match.89-2.479J ISSN: 0340-6253 2023 info:eu-repo/semantics/article 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.