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 Rα(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. Copyright © 2016 John Wiley & Sons, Ltd. In this paper, we study hex‐derived networks HDN1(n) and HDN2(n), which are generated by a hexagonal network of dimension n and derive analytical closed results of general Randić index Rα(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.