On Topological Indices for New Classes of Benes Network

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 HCB(r) 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 Randic connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity (VCB(r)), and geometric arithmetic (ABC) index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.

Automated summary

The paper explored two classes of Benes networks and derived closed-form expressions for some of their topological indices. Additionally, the fourth version of GA and the fifth version of ABC indices were calculated for these network classes.