The study of pentagonal chain with respect to schultz index, modified schultz index, schultz polynomial and modified schultz polynomial.

Distance-based topological indices are numerical parameters that are derived from the distances between atoms in a molecular structure, and they provide a quantitative measure of the topology and geometry of a molecule. The distance-based topological indices uses to predict various properties of molecules, including their boiling points, melting points, and solubility. It also predicts the biological activity of molecules, including their pharmacological and toxicological properties. Pentagonal chain molecules are organic compounds that consist of a linear chain of five-membered (pentagons) connected by carbon and bonds. These molecules have unique structural and electronic properties that make them useful in a variety of applications. Motivated by the pentagonal chain molecules, we have considered a pentagonal chain graph and it is denoted by Pn. We have computed some distance based topological indices for Pn. The paper focuses on a pentagonal chain molecules denoted by G, and derives several distance-based topological indices. These indices compromise insights into physicochemical properties, aid in identifying structural characterizations, and enhance understanding of molecular properties.