Bismuth tri-iodide \((BiI_3)\) is a structurally flexible inorganic compound and shows high potential in the field of materials science owing to the many chain and sheet configurations it can form. In the present work, we carry out an in-depth topological characterization of \((BiI_3)\) on the basis of ev-degree and ve-degree-based descriptors, providing insight into its molecular structure by applying graph-theoretical methods. Using symbolic computation and visualization through MATLAB, we calculate and examine a set of topological descriptors ranging from the Zagreb, Randic, Atom-Bond Connectivity, and Geometric-Arithmetic indices for the chain \((BiI_3)\) and the sheet \((BiI_3)\) forms. We then statistically examine the properties and relate them with the topological descriptors through the help of QSPR models. We find high correlations between the branching parameters and the topological indices, reflecting the potential for prediction. We emphasize the practical application of degree-based descriptors in molecular connectivity and explicate the potential for the design of structural descriptors in inorganic compounds in the fields of nanotechnology and materials science.
