On topological indices of poly oxide, poly silicate, DOX, and DSL networks

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom-bond connectivity (ABC), and 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 different interconnection networks and derive analytical closed results of the general Randić index (R_α(G)) for α = 1, 12,-1, -12 only, for dominating oxide network (DOX), dominating silicate network (DSL), and regular triangulene oxide network (RTOX). All of the studied interconnection networks in this paper are motivated by the molecular structure of a chemical compound, SiO₄. We also compute the general first Zagreb, ABC, GA, ABC₄, and GA₅ indices and give closed formulae of these indices for these interconnection networks.