Modified Zagreb Connection Indices for Benes Network and Related Classes

Abstract

The study of networks such as Butterfly networks, Benes networks, interconnection networks, David-derived networks through graph theoretical parameters is among the modern trends in the area of graph theory. Among these graph theoretical tools, the topological Indices TIs have been frequently used as graph invariants. TIs are also the essential tools for quantitative structure activity relationship (QSAR) as well as quantity structure property relationships (QSPR). TIs depend on different parameters, such as degree and distance of vertices in graphs. The current work is devoted to the derivation of 2-distance based TIs, known as, modified first Zagreb connection index ZC 1 ? and first Zagreb connection index ZC 1 for r ? dimensional Benes network and some classes generated from Benes network. The horizontal cylindrical Benes network HCB r , vertical cylindrical Benes network VCB r , and toroidal Benes network TB r are the three classes generated by identifying the vertices of the first row with the last row, the first column with the last column of the Benes network. The obtained results are also analyzed through graphical tools.