Unique Studies of Butterfly Graph

Butterfly distribution plays a very important role while mining metals and fuels in various ways. Availability of metals, minerals, fuels can be found using the techniques/studies of Butterfly graph. We investigate the unique studies of Butterfly graph like its Characteristic polynomial, Complement, Graph Indices, Discrete Fourier transform of Diameter, Girth, Vertex connectivity and Edge connectivity using Fast Fourier Transform algorithm (Butterfly method), QR-Decomposition, its regular stochastic matrix and optimal prefix code of a Butterfly graph.