The molecular structure of hydroxychloroquine (HCQ) used in the treatment of malaria is recently suggested for emergency used in COVID-19. The chemical compound of HCQ is produced by chemical alteration of ethylene oxide from human products, such as waxy maize starch. The molecular graph is a graph comprising of atoms called vertices and the chemical bond between molecules is called edges. A topological index is a numerical representation of a chemical structure which correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. To distinguish the creation of entropy-based measures from the structure of chemical graphs, several graph properties have been utilized. For computing the structural information of chemical graphs, the graph entropies have become the information-theoretic quantities. The graph entropy measure has attracted the research community due to its potential application in discrete mathematics, biology, and chemistry. In this paper, our contribution is to explore graph entropies for molecular structure of HCQ based on novel information function, which is the number of different degree vertices along with the number of edges between various degree vertices. More precisely, we have explored the degree-based topological characteristics of hydroxyethyl starch conjugated with hydroxychloroquine (HCQ–HEC). Also, we computed entropies of this structure by making a relation of degree-based topological indices with the help of information function. Moreover, we presented the numerical and graphical comparison of the computed results.

A graph invariant is a numerical value that depicts the structural properties of an entire graph. The Wiener index is the oldest distance based graph invariant which is defined as the sum of distances between all unordered pair of vertices of the graph G. In this paper we use the method of edge cut to compute the Wiener index and Wiener polarity index of linear (L_n) and zig-zag (Z_n) polyomino chains of 4-cycle. Also, we introduce another polyomino chain of 4k-cycle Z_mn and calculate its Wiener index and Wiener polarity index for m = 3 and m = 4. Finally, the graphical representation is given to analyze the behavior of these indices.

The bismuth tri-iodide $(Bi{I}_3)$ is an inorganic compound. It is the result of the response of bismuth and iodine, which has inspired enthusiasm for subjective inorganic investigation. The topological indices are the numerical invariants of the molecular graph that portray its topology and are normally graph invariants. In 1975, Randic presented, in a bond-added substance, a topological index as a descriptor for portraying subatomic branching. In this paper, we investigate the precious stone structure of bismuth tri-iodide chain and sheet. Moreover, exact formulas of degree-based added-substance topological indices principally the first, second, and hyper Zagreb indices, the general Randic index, the geometric-arithmetic index, the fourth atom-bond connectivity index, and the fifth geometric arithmetic index of the subatomic graph of bismuth tri-iodide for both chain and sheet structures are determined.

The Chemical graph theory is extensively used in finding the atomic supplementary properties of different chemical stuructures. Many results of graph theory are commonly used in molecular structures and in general in Chemisty. In a molcular graph vertices are atoms while chemical bonds are given by edges. This article is about computing the exact values for some degree based toplogical descriptors of two molecular structures. Namely we work on the silicon-carbon Si₂C₃- III and SiC₃-III for dimension two. We also discuss some applications of these results towards Chemistry.

A variety of dendrimers exist, and each has biological properties such as polyvalency, selfassembling, electrostatic interactions, chemical stability, low cytotoxicity, and solubility. These varied characteristics make dendrimers a good choice in the medical field and pharmaceuticals. A topological index is actually designed by transforming a molecular structure into a numeric number. These topological indices correlate certain physicochemical properties like boiling point, stability, strain energy etc of chemical compounds. It is reported that these indices are useful in the study of anti-in ammatory activities, anticancer therapies and diagnostic imaging of certain chemical networks. In this paper, we determine hyper Zagreb index, first multiple Zagreb index, Second multiple Zagreb index, Zagreb polynomials for nanostar dendrimers, Benzenoid and phenylenes.