o:28961 Sombor energy and Huckel rule en 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. Keywords: energy (of a graph), Sombor index, Sombor energy, graph energy, topological index, degree (of a vertex) 1552099 10.47443/dml.2021.s211 1552101 2664-2557 2023-04-29T08:02:47.306Z 44 no 46 Ivan Gutman 0000-0001-9681-1550 Izudin Redžepović Državni univerzitet u Novom Pazaru person 0000-0003-4956-0407 application/pdf 476807 https://phaidrabg.bg.ac.rs/o:28961 no yes 16 70 92000001 20A01 Discrete Mathematics Letters 9 67 71 2022