On Topological Indices for New Classes of Benes Network

Abstract

Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network $\text{HCB}\left(r\right)$ and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( $\text{VCB}\left(r\right)$ ), and geometric arithmetic $\left(\text{ABC}\right)$ index of the two classes of Benes networks. Also, the fourth version of $\text{GA}$ and the fifth version of $\text{ABC}$ indices are computed for these classes of networks.