Investigation of Topological properties of Butterfly Networks by Irregularity Invariants

In the modern era, networks play a crucial role in connecting individuals, organizations, and devices, enabling efficient communication, collaboration, and information exchange across the globe. They serve as the backbone of the digital age, supporting the growth of technologies such as the internet, cloud computing, IoT, and social media. The examination of Quantitative Structure Activity/Property Relationships (QSPR) to analyze the network architecture uses topological indices as its main instrument. The butterfly network is a type of interconnection network that follows a specific geometric structure. It consists of multiple stages, with each stage connecting nodes in a binary pattern. The connections between nodes form a butterfly-like shape, hence the name. The butterfly network provides efficient routing and communication paths between nodes, making it suitable for parallel computing and distributed systems. With the aid of sixteen irregularity indices, we will examine and compare three butterfly networks in this article. We will then plot the findings to see how they depend on the various parameters.