Exact Distance-Based Topological Indices Of Double Star Double Fanbell Graphs With Applications In Chemical Graph Theory, QSPR/QSAR Modeling, And Drug Discovery

Abstract

The topological indices are fundamental tools in chemical graph theory with the aim of numerically describing the structural properties of molecular graphs and also predicting physicochemical and biological parameters. In this paper, we present a new graph family called Double Star Double Fanbell (BSDF) which consists of double star graph with each pendant vertex added with a double fan graph. Eight important distance based topological indices are considered, namely Wiener index, Hyper-Wiener index, Harary index, Reciprocal Complementary Wiener index, Wiener Polarity index, Terminal Wiener index, Reverse Wiener index, and Reciprocal Reverse Wiener index are considered and exact closed-form expressions are obtained. The analytical formulations are derived by a systematic distance-partitioning method and written in terms of the graph parameters, which allows the formula to be computed efficiently for any graph size without a need for any repeated shortest-path computations.

In addition to their mathematical importance, the calculated topological descriptors are useful molecular descriptors in Chemical Graph Theory, in which atoms are depicted as vertices, and chemical bonds as edges. These descriptors can be used effectively in Quantitative Structure–Property Relationship (QSPR) and Quantitative Structure–Activity Relationship (QSAR) models to predict molecular stability, boiling point, melting point, solubility, lipophilicity, biological activity, toxicity and pharmacokinetic properties. Moreover, the proposed BSDF graph provides a proper model for the highly branched organic compounds, dendrimer, hyperbranched polymers, and functional nanomaterials. Expressions obtained in this work are in an exact form, which is very appealing for large scale molecular databases, virtual screening, cheminformatics and AI-assisted drug discovery. Therefore, the suggested graph is not only playing a theoretical role in advancement of graph theory but also in the present day computational chemistry and pharmaceutical research.