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 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 (), and geometric arithmetic index of the two classes of Benes networks. Also, the fourth version of and the fifth version of indices are computed for these classes of networks.

中文翻译：

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Benes网络新类的拓扑指标

拓扑指数（TIs）将分子图转换为数字。TI是用于定量结构活动关系（QSAR）和数量结构性质关系（QSPR）的重要工具。在本文中，我们构造了两类Benes网络：分别通过识别Benes网络的最后一行的第一行和最后一列的第一列的顶点来获得水平圆柱Benes网络和垂直圆柱Benes网络。我们推导了广义Randić连通性指数，广义Zagreb，第一和第二Zagreb（以及乘性Zagreb），广义和连通性，原子键连通性（）以及两类Benes网络的几何算术指数的解析式。另外，第四版为这些类别的网络计算索引的第五个版本。