On topological properties of poly honeycomb networks

Abstract

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 Randic, 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 Randic index \(R_\alpha (G)\) for different values of \(\alpha \), for a David derived network \((\textit{DD}(n))\) of dimension n, a dominating David derived network \((\textit{DDD}(n))\) of dimension n as well as a regular triangulene silicate network of dimension n. We also compute the general first Zagreb, ABC, GA, \(\textit{ABC}_4\) and \(\textit{GA}_5\) indices for these poly honeycomb networks for the first time and give closed formulas of these degree based indices in case of poly honeycomb networks.