TOPOLOGICAL INDICES OF MOLECULAR GRAPHS AND THEIR APPLICATIONS TO STRUCTURE-PROPERTY PREDICTION
Chemical graph theory supplies a compact mathematical representation of molecular structure by treating atoms as vertices and chemical bonds as edges. In this paper, several classical and contemporary topological indices are organized into a unified framework for molecular graphs, with emphasis on their use as interpretable descriptors in quantitative structure-property relationship (QSPR) modelling. Degree-based, distance-based and mixed descriptors are reviewed, exact expressions are derived for path, cycle and star molecular graph families, and a reproducible descriptor-to-property modelling protocol is formulated. The results show how the Wiener, Zagreb, Randić, atom-bond connectivity and geometric-arithmetic indices encode size, branching and local bond-environment effects. These descriptors provide a mathematically transparent basis for preliminary structure-property screening, provided that statistical validation and chemical interpretability are both maintained.