Abstract
Polymers, drugs, and almost all chemical or biochemical compounds are frequently modeled as diverse ω -cyclic, acyclic, bipartite, and polygonal shapes and regular graphs. Molecular descriptors (topological indices) are the numerical quantities and computed from the molecular graph Γ (2D lattice). These descriptors are highly significant in quantitative structure-property or activity relationship (QSPR and QSAR) modeling that provides the theoretical and the optimal basis to expensive experimental drug design. In this paper, we study three isomeric natural polymers of glucose (polysaccharides), namely, cellulose, glycogen, and amylopectin (starch), having promising pharmaceutical applications, exceptional properties, and fascinating molecular structures. We intend to investigate and compute various closed-form formulas such as ABC , GA , sum-connectivity χ − 1 / 2 , ABC 4 , GA 5 , and Sanskruti indices for the aforementioned macromolecules. Also, we present the closed-form formulas for the first, second, modified, and augmented Zagreb indices, inverse and general Randić indices, and symmetric division deg, harmonic, and inverse sum indices. Furthermore, we provide a comparative analysis using 3D graphs for these families of macromolecules to clarify their nature.
Highlights
Cheminformatics is a comparatively new area of information technology that comprises chemistry, mathematics, and other informational sciences that concentrate on gathering, storage, treatment, and examination of chemical data
In [5], Gutman and Trinajsticproposed two degreebased invariants known as the first Zagreb index (FZI) M1 and the second Zagreb index (SZI) M2. ese indices initially appeared in the expression of the total π-electron of the molecular graph and were later applied to study molecular complexity and ZE isomerism. e formulas of M1, M2, and the modified Zagreb index (MSZI) are given as
We explain the chemical structure of cellulose, in general, and convert it into a mathematical object called a molecular graph to investigate its properties using tools from graph theory. It comprises over 3, 000 D-glucose units that are linked by β(C1 − C4) glycosidic bonding and have general formula (C6H10O5)n
Summary
Cheminformatics is a comparatively new area of information technology that comprises chemistry, mathematics, and other informational sciences that concentrate on gathering, storage, treatment, and examination of chemical data. We develop the polymeric graphs of three closely related natural polymers (isomeric), broadly known as cellulose, glycogen, and amylopectin, to compute certain invariants to anticipate their physicochemical properties. For cellulose network CLnm, the formulas for the modified second Zagreb, inverse Randic, harmonic, inverse sum, and augmented Zagreb indices are
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