o:28906 On the Conjecture Related to the Energy of Graphs with Self–Loops en 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 spectrum, energy of graphs, energy of graphs with self-loops 1552099 10.46793/match.89-2.479J 1552101 0340-6253 2023-04-24T08:26:45.836Z 44 no 46 Irena M. Jovanović 0000-0003-0819-7111 Emir Zogić Državni univerzitet u Novom Pazaru person 0000-0002-1355-3785 Edin Glogić Državni univerziet u Novom Pazaru person 0000-0001-6295-8298 application/pdf 486118 https://phaidrabg.bg.ac.rs/o:28906 no yes 1 70 92000001 20A01 MATCH Communications in Mathematical and in Computer Chemistry 89 2 479 488 2023