The Solution of Faculty Selection Problem Using the Concept of Edge Coloring of m-polar Fuzzy Graph

Abstract

Edge colouring for crisp graphs is a well-defined topic. However, fuzzy graph edge coloring was very recently developed. In a m-polar fuzzy network, however, we have to take into account m components for each node and edge. Since this idea has just one component, we cannot handle this kind of circumstance with a fuzzy model for we consider m components for both nodes and edges in our consideration. Again, we cannot utilize the bipolar or intuitionistic models because every edge or node in the fuzzy network consists of simply two components. Therefore, these mPFG models yield fuzziness discoveries more effectively than earlier fuzzy models. Additionally, creating and examining these kinds of mPFGs with instances and associated theorems is quite intriguing. Considering all those things together, defining edge colouring for mPFG needs some new ideas. In this article, we studied edge colouring for mPFG along with many interesting associated properties. Here, the chromatic index as well as its generalizations and interconnected facts are thoroughly investigated. Here, we also find chromatic numbers as well as strong chromatic numbers on some well-known mPFG. A relation between chromatic numbers and the strong chromatic number has been discussed here. We also give an alternative form of edge colouring with the help of node colouring based on the mPF line graph. Both processes have been discussed thoroughly in step-by-step methods along with prescribed examples. We introduced an algorithm for edge colouring on mPFG. Lastly, a real-life application based on edge colouring for mPFG has been discussed to show the usefulness of the proposed method.