A comparison between certain graph parameters of biswapped networks and their maximal twin-preserving subgraphs with applications in determining complexity

The study of different objects, such as the properties of algebraic structures, the analysis of chemical graph structures without experiment, and understanding networks through topological indices (TIs), is among the modern directions in graph theory. The analysis of different networks, such as the Benes network, butterfly network, hex-derived network and biswapped network, using TIs is one of the modern research fields. The storage and transfer of data carrying certain information has always remained a modern world problem. The optoelectronic technology used in optical transpose interconnection systems (OTIS) is efficient in outcome over an electrical system due to the minimum power consumption and broad bandwidth. By combining the use of wireless and electrical technologies, OTIS has developed into a valuable network and boosted the efficiency of contemporary optoelectronic computers. A special type of OTIS is the biswapped network over the path graph P n , denoted by B ( P n ) . In this article, a maximal twin-preserving subgraph of a biswapped network over the path graph P n is constructed. Moreover, the biswapped network B ( P n ) and its constructed subgraph are compared through ev-degree- and ve-degree-dependent TIs. In addition to this, to analyse the complexity of B ( P n ) and M T ( B ( P n ) ) through information functional-based entropies, we define ve-degree- and ev-degree-based information functionals and compute formulae for ve-degree- and ev-degree-based entropies. The analytical formulae, tables and graphical trends are used to describe a comparison between the TIs and entropies of B ( P n ) and M T ( B ( P n ) ) . It is shown that the values of TIs and entropies only differ by a constant depending on the value of n .