On topological indices of certain interconnection networks

• We derive analytically closed results of certain degree based topological indices for butterfly and Benes networks.
• We define two new families of mesh derived networks by using some basic operations on graphs.
• We compute exact formulas of certain degree based topological indices for newly defined mesh derived networks.

In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC)(ABC) and geometric-arithmetic (GA)(GA) index are used to predict the bioactivity of chemical compounds. A topological index is actually designed by transforming a chemical structure into a numeric number. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc of chemical compounds. Graph theory has found a considerable use in this area of research.The topological properties of certain networks are studied recently in [13] by Hayat and Imran (2014). In this paper, we extend this study to interconnection networks and derive analytical closed results of general Randić index Rα(G)Rα(G) for different values of “αα” for butterfly and Benes networks. We also compute first Zagreb, ABC, and GA   indices for these important classes of networks. Moreover, we construct two new classes of mesh derived networks by using some basic operations of graphs on m×nm×n mesh networks, and then study certain topological indices for these classes of networks.