On topological properties of poly honeycomb networks

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as the Randić, the atom-bond connectivity (ABC) and the geometric-arithmetic (GA) indices 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 poly honeycomb networks which are generated by a honeycomb network of dimension n and derive analytical closed results for the general Randić index R_α(G) for different values of α, for a David derived network (DD(n)) of dimension n, a dominating David derived network (DDD(n)) of dimension n as well as a regular triangulene silicate network of dimension n. We also compute the general first Zagreb, ABC, GA, ABC₄and GA₅indices for these poly honeycomb networks for the first time and give closed formulas of these degree based indices in case of poly honeycomb networks.