A topological index is a number that is connected to a chemical composition in order to correlate a substance’s chemical makeup with different physical characteristics, chemical reactivity, or biological activity. It is common to model drugs and other chemical substances as different forms, trees, and graphs. Certain physico-chemical features of chemical substances correlate better with degree-based topological invariants. Predictions concerning the dynamics of the continuing pandemic may be made with the use of the graphic theoretical approaches given here. In Networks, the degree entropy of the epidemic and related trees was computed. It highlights the essay’s originality while also implying that this piece has improved upon prior literature-based realizations. In this paper, we study an important degree-based invariant known as the inverse sum indeg invariant for a variety of graphs of biological interest networks, including the corona product of some interesting classes of graphs and the pandemic tree network, curtain tree network, and Cayley tree network. We also examine the inverse sum indeg invariant features for the molecular graphs that represent the molecules in the bicyclic chemical graphs.

Fenofibrate is a drug approved by FDA Food and Drugs Administration used to treat patients with Hypertrigly ceridemia primary hypercholesterolemia or mixed dyslipidemia. It reduces low-density lipoprotein cholesterol (LDL-c), total cholesterol, triglycerides, and apolipoprotein B and increases high -density lipoprotein cholesterol (HDL-C) in adults. The sum and multiplicative versions of several topological indices such as General Zagreb, General Randic, Arithmetic Geometric Index, Inverse sum (Indeg) Index, Symmetric Division (Deg) Index, Forgotten Indices M-polynomials of Fenofibrate are computed in this article.

A numerical invariant that describes the topology of a graph G is known a topological index. The topological indices are ideal tools that can be used for analysing the structure of molecular graphs as it reflects the chemical properties of the molecules. In this article, the drugs used in the treatment of peripheral neuropathy are analysed with the help of topological indices and a QSPR analysis is done. The degree based topological indices are used for this structural analysis of chemical compounds of these drugs. The graph structure of a chemical component is derived from a chemical component by considering the toms as vertices and the bonds connecting two atoms as edges, the edge-partitions are noted and computed the topological indices. The correlation among the chemical properties of the drugs and the topological indices are computed. A detailed diagrammatic illustration of these correlation analyses is done. These comprehensive analyses may help scientists and chemist working in the drug design of peripheral neuropathy.

In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product of graphs and compute the Y index of new operations of graphs related to the join of graphs.

The reduced Sombor index is a modified version of the very famous Sombor Index for a graph ????. In this article, the reduced Sombor index is studied on various classes of graphs and novel results on the bounds of the reduced Sombor index of graphs are obtained. The graphs with minimum reduced Sombor index are studied, and the graphs achieving certain bounds are found.