Computation and Analysis of Degree and Neighbourhood Degree Sum Based Topological Descriptors for Certain Chemical Structures

Abstract

Over the past 50 years, graph theory and information theory have helped theoretical chemistry describe molecular structures. Topologically characterizing chemical structures enables us to organize molecules and simulate unknown structures with desired attributes. Topological indices are numerical parameters of a molecular graph that characterise the bonding topology of a molecule and are necessarily structure invariant. The main goal of studying topological indices is to capture and transform the information contained in a chemical structure and develop a mathematical relationship between the structures and physico-chemical properties, bio-activities, and other experimental properties of the chemicals. Topological indices are used in the development of Quantitative Structure-Property Relationships (QSPRs) and Quantitative Structure-Activity Relationships (QSARs) in which a large number of molecular properties ranging from physico-chemical and thermodynamic properties to chemical activity and biological activity are correlated with their chemical structures. newline In this study, we define new degree-based and neighbourhood degree sum-based topological indices, namely: Reduced Reverse Degree Based Indices, Open and Closed neighbourhood versions of degree-based topological descriptors. We have performed QSPR and QSAR analysis using single variate regression models and multi-variate regression models for different chemical compounds like Octane isomers, Monocarboxylic acids, Benzenoid Hydrocarbons, COVID-19 drugs, cyclic p-terphenyls 9 and 11 and functionalized stilbenes 11. The best-fit models are identified based on R2 and Root Mean Squared Error (RMSE) values. Further, the established models are validated using Chi-square and#967;2 - goodness of fit test. We have also calculated these topological indices for materials used in industries namely, Graphene structure, Metal-Organic Frameworks and materials used in cancer treatment, namely, Hyaluronic Acid-Curcumin conjugates and Hyaluronic Acid-Paclitaxel conjugates. newline newline