Ordering chemical graphs by Sombor indices and its applications

Abstract

Topological indices are a class of numerical invariants that predict certain physical and chemical properties of molecules. Recently, a novel topological index, named as Sombor index, was introduced by Gutman, defined aswhere d u denotes the degree of vertex u.In this paper, our aim is to order the chemical trees, chemical unicyclic graphs, chemical bicyclic graphs and chemical tricyclic graphs with respect to their Sombor index. We find the first fourteen minimum chemical trees, the first four minimum chemical unicyclic graphs, the first three minimum chemical bicyclic graphs, the first seven minimum chemical tricyclic graphs.

Normalized Sombor indices as complexity measures of random graphs

“…5(e,f), the curves of the main panels are now properly scaled when plotted as a function of p. k = np/2, we get exactly the same expressions listed in Eqs. (13)(14)(15)(16)(17). This is verified in Figs.…”

“…Moreover, the applicability of Eqs. (13)(14)(15)(16)(17) to the three random graph models we study here allow us to relate the average value of a…”

“…Even though Sombor indices were introduced very recently, there are already several works available in the literature where these indices are applied to chemical graphs of interest, see e.g. [4,5,[7][8][9][10][11][12][13][14][15][16][17][18]. Also, bounds for Sombor indices as well as relations among them and with many other topological indices have been reported in [4,10,[19][20][21][22][23][24].…”

On Sombor index of graphs with a given number of cut-vertices

“…Successful predictive potential of the Sombor index has also been employed for simulating the thermodynamic characteristics of organic compounds. The reader is referred to [1,2,3,4,5,6,7,8,9,10,11,13,16,17,18,19,20,21,22,23,24,26,27,30], for a detailed mathematical treatment of the Sombor index of graphs.…”

The Sombor index of trees and unicyclic graphs with given maximum degree

“…Deng et al [3] obtained a sharp upper bound for the Sombor index among all molecular trees with fixed numbers of vertices, and characterized those molecular trees achieving the extremal value. Liu [10] determined the first fourteen minimum chemical trees, the first four minimum chemical unicyclic graphs, the first three minimum chemical bicyclic graphs, the first seven minimum chemical tricyclic graphs. Réti et al [14] characterized graphs with the maximum Sombor index in the classes of all connected unicyclic, bicyclic, tricyclic, tetracyclic, and pentacyclic graphs of a fixed order.…”