On certain topological indices of octahedral and icosahedral networks

Abstract

The authors have computed topological indices of two metal-organic frameworks of considerable interest in reticular chemistry, namely octahedral and icosahedral networks. The topological indices of these metal-organic frameworks are extremely useful not only in the characterisation of these complex networks but also in obtaining correlation relationships of a number of their properties. In this study, they have obtained exact analytical expressions for a large number of topological indices such as the Randić index, Zagreb index, harmonic index, sum-connectivity index, atom-bond connectivity index, geometric-arithmetic index and their corresponding variants for the two newly constructed networks. Furthermore, they have used the recently introduced partition method by the transitive closure of Djoković-Winkler relation to obtain the Wiener indices for the chain and even cyclic octahedral and icosahedral frameworks with an observation that this method is not successful in computing the Wiener index of these two networks and they pose an open problem for the same.