Abstract
A chemical graph is a model used to indicate a chemical combination. In a molecular graph, vertices define atoms, and edges are represented as chemical bonds. A topological index is a single number to characterize the graph of a molecule. In this article, we study the topological properties of some special chains. The polyphenyl chains with hexagons are graphs of aromatic organic compounds. The key purpose of this article is to explore the expected value of Sombor, reduced Sombor, and average Sombor index for this category of organic compounds. It was investigated that the Sombor, reduced Sombor and average Sombor index revealed adequate discriminative potential of alkanes. It has been tested that these indicators can be used effectively in modeling chemical thermodynamic structures. The average value of the Sombor, reduced Sombor, and average Sombor index for the set of all spiro and random polyphenyl chains has been determined. Finally, the ratio between the expected values of these mentioned indices for both random chains has been resolved. Doi: 10.28991/ESJ-2022-06-01-012 Full Text: PDF
Highlights
Aromatic organic compounds are main building blocks for many natural and synthetic chemical compounds as well as constituents of petrochemicals
There is a Hosoya index, which is calculated by counting non-incident edges on a graph
The degree based topological index play an important part in chemical graph theory
Summary
Aromatic organic compounds are main building blocks for many natural and synthetic chemical compounds as well as constituents of petrochemicals. We symbolize the anticipated values of these indices byEkSO = ESO [SO (ŔSC(k; ζ1, ζ2))] , Ekred = Ered [SOred (ŔSC(k; ζ1, ζ2))] and Ekavg = Eavg [SOavg (ŔSC(k; ζ1, ζ2))] respectively. In this part, the average value of SO, SOred and SOavg have been resolved for the set of arbitrary spiro chain. By getting results from theorem (5-1, 5-2) and (5-3), we will make the ratio between the expected values for the SO, SOred and SOavg with the same probabilities ζ1 and ζ2 of a random spiro-chain.
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