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 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 Randić 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.
Highlights
Graphs are used to design interconnected networks in a very natural way, in which the processors or components represent vertices and edges represent the communication links, e.g., fiber optic cables. e way in which all these components work will be carried out by incidence functions
Ere are series of interconnection patterns and switching stages in a butterfly network that permits n inputs to be linked to n outputs. e Benes network consists of butterflies connected back to back. e Benes network is known for permutation routing [2]. ey are significant multistage interconnection networks, which enjoy striking topologies for communication networks [3]. e use of Benes network is in parallel computing systems such as SP1/SP2, IBM, NEC Cenju-3, and MIT Transit Project
Let H be the graph of horizontal cylindrical Benes network (HCB(r))
Summary
Aftab Hussain ,1 Muhammad Numan ,2 Nafisa Naz ,2 Saad Ihsan Butt ,3 Adnan Aslam ,4 and Asfand Fahad 5. Graphs are used to design interconnected networks in a very natural way, in which the processors or components represent vertices and edges represent the communication links, e.g., fiber optic cables. E use of Benes network is in parallel computing systems such as SP1/SP2, IBM, NEC Cenju-3, and MIT Transit Project. Ere are series of interconnection patterns and switching stages in a butterfly network that permits n inputs to be linked to n outputs. It is used in the internal structures of optical couplers [4, 5]. Ere are 2r + 1 levels in an r-dimensional Benes network where every level has 2r nodes.
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