Analytical expressions for topological properties of polycyclic benzenoid networks

Quantitative structure-activity and structure-property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks. Structure-based topological indices of these networks enable prediction of chemical properties and the bioactivities of these compounds through quantitative structure-activity and structure-property relationships methods. We consider a number of infinite convex benzenoid networks that include polyacene, parallelogram, trapezium, triangular, bitrapezium, and circumcorone series benzenoid networks. For all such networks, we compute analytical expressions for both vertex-degree and edge-based topological indices such as edge-Wiener, vertex-edge Wiener, vertex-Szeged, edge-Szeged, edge-vertex Szeged, total-Szeged, Padmakar-Ivan, Schultz, Gutman, Randic, generalized Randic, reciprocal Randic, reduced reciprocal Randic, first Zagreb, second Zagreb, reduced second Zagreb, hyper Zagreb, augmented Zagreb, atom-bond connectivity, harmonic, sum-connectivity, and geometric-arithmetic indices. In addition we have obtained expressions for these topological indices for 3 types of parallelogram-like polycyclic benzenoid networks.