An Investigation on M-Polar Fuzzy Saturation Graph and Its Application

Abstract The saturation graph is a well-defined topic. But, saturation in a fuzzy graph was de ned recently and investigated many properties. In a fuzzy saturation graph, only one saturation is considered for every vertex. In a m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining saturation for mPFG is not easy and needs some new ideas. By considering m saturation for each component out of m components of membership values of a vertex, we defined saturation in mPFG. α-saturation as well as β-saturation in mPFG is introduced here. Many interesting properties of it are also presented. α-vertex count and β-vertex count in mPFG are also studied and the upper bound on some well known mPFG is also found here. Finally, a real-life application using saturation in mPFG is also presented.