najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2021-12-4-411-417najo-454Research ArticleMATHEMATICSМАТЕМАТИКАOn Sombor energy of graphsОб энергии Сомбора графовGowthamK. J.GowthamK. J.

Dept. of Mathematics, 

Tumakuru, Karnataka State, Pin 572 103.

Dept. of Mathematics,

Tumakuru, Karnataka State, Pin 572 103.

gowtham_k_j@yahoo.comSwamyNarahari NarasimhaSwamyNarahari Narasimha

Dept. of Mathematics, 

Tumakuru, Karnataka State, Pin 572 103.

Dept. of Mathematics,

Tumakuru, Karnataka State, Pin 572 103.

narahari_nittur@yahoo.comTumkur University, University College of ScienceTumkur University, University College of Science202104082025124411417Copyright © Gowtham K.J., Swamy N.N., 20252025Gowtham K.J., Swamy N.N.Gowtham K.J., Swamy N.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/454

The concept of Sombor index SO(G) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by SO(G). This paper introduces a new matrix for a graph G, called the Sombor matrix, and defines a new variant of graph energy called Sombor energy ES(G) of a graph G. The striking feature of this new matrix is that it is related to well-known degree-based topological indices called forgotten indices. When ES(G) values of some molecules containing hetero atoms are correlated with their total πelectron energy, we got a good correlation with the correlation coefficient r = 0.976. Further, we found some bounds and characterizations on the largest eigenvalue of S(G) and Sombor energy of graphs.

Понятие индекса Сомбора SO(G) было недавно введено Гутманом в химическую теорию графов. Это топологический индекс, основанный на степени вершины, и он обозначается SO(G). В этой статье вводится новая матрица для графа G, называемая матрицей Сомбора, и определяется новый вариант энергии графа, называемый энергией Сомбора ES(G) графа G. Поразительной особенностью этой новой матрицы является то, что она хорошо связана с  известными топологическими индексами на основе степеней, называемыми забытыми индексами. Когда значения ES(G) некоторых молекул, содержащих гетероатомы, коррелируют с их полной энергией π-электронов, мы получили хорошую корреляцию с коэффициентом корреляции r = 0,976. Далее мы нашли некоторые оценки и характеристики наибольшего собственного значения S(G) и энергии Сомбора графов.

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The authors declare that there are no conflicts of interest present.