On molecular topological properties of hex-derived networks

Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure-activity relationship/quantitative structure-property relationship study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC), and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study hex-derived networks HDN1(n) and HDN2(n), which are generated by hexagonal network of dimension n and derive analytical closed results of general Randić index R_α(G) for different values of α, for these networks of dimension n. We also compute the general first Zagreb, ABC, GA, ABC₄, and GA₅ indices for these hex-derived networks for the first time and give closed formulae of these degree-based indices for hex-derived networks.