2022 eng https://phaidrabg.bg.ac.rs/o:28961 doi:10.47443/dml.2021.s211 ISSN: 2664-2557 Discrete Mathematics Letters 9 Sombor energy and Huckel rule http://creativecommons.org/licenses/by/4.0/legalcode Keywords: energy (of a graph), Sombor index, Sombor energy, graph energy, topological index, degree (of a vertex) info:eu-repo/semantics/article Gutman, Ivan Redžepović, Izudin Abstract: The Sombor index, a recently invented vertex-degree-based graph invariant, is insensitive to the size of cycles contained in a graph. In contrast to this, the Sombor energy, the sum of absolute values of the Sombor matrix, is found to have a significant cycle-size dependence. In the case of bipartite graphs, this dependence is analogous to the Huckel (4n + 2)-rule: cycles of size 4, 8, 12, . . . decrease, and cycles of size 6, 10, 12, . . . increase the Sombor energy. A theorem corroborating this empirical observation is offered. application/pdf 476807 bytes