Topological Study of Line Graph of Remdesivir Compound Used in the Treatment of Corona Virus

The expected values of the total numbers of independent edge sets and independent sets in random alpha-type pentagonal chains

A independent edge set of G containing mutually independent edges is also called a matching of G. The total numbers of matchings and independent sets of a graph G, namely, the Hosoya index and the Merrifield-Simmons index, respectively, are two important topological indices. We compute the average total numbers of independent edge sets and independent sets in random alpha-type pentagonal chains.

Analysis of a Productive Topological Index Correlated to Fullerenes’ Physical Properties

Fullerene is a cage-like carbon allotrope admitting a vast range of applications. Some of the important fullerenes are C54,C58,C60,C70,C74,C76,C78,C80C82,C84,C86,C90. The physical properties of fullerenes can be exhibited using the degree-based topological indices. The sum based geometric arithmetic index is significant in this manner. The sum based atomic bond connectivity, Randic, first and second Zagreb indices are well known topological indices. We have determined the regression relation between each of these indices and the sum based geometric arithmetic index. Moreover, the correlation coefficient is also calculated. Correlation is a symmetric relation, as it provides association between two variables. On the basis of regression analysis and correlation coefficient, it was found that each of this index is strongly related to the sum based geometric arithmetic index. Moreover, we have computed the regression relations concerning the physical properties depending on the sum based geometric arithmetic index. The physical properties include binding energies, Ramsauer-Townsend minima, shape resonances and heat of formation of fullerene molecules. It was concluded that the sum based GA index is the best in presenting the heat of the formation of molecules.