Abstract
In this research study, we first define the strong degree of a vertex in an m-polar fuzzy graph. Then we present various useful properties and prove some results concerning this new concept, in the case of complete m-polar fuzzy graphs. Further, we introduce the concept of m-polar fuzzy strength sequence of vertices, and we also investigate it in the particular instance of complete m-polar fuzzy graphs. We discuss connectivity parameters in m-polar fuzzy graphs with precise examples, and we investigate the m-polar fuzzy analogue of Whitney's theorem. Furthermore, we present a clustering method for vertices in an m-polar fuzzy graph based on the strength of connectedness between pairs of vertices. In order to formulate this method, we introduce terminologies such as epsilon(A)-reachable vertices in m-polar fuzzy graphs, epsilon(A)-connected m-polar fuzzy graphs, or epsilon(A)-connected m-polar fuzzy subgraphs (in case the m-polar fuzzy graph itself is not epsilon(A)-connected). Moreover, we discuss an application for clustering different companies in consideration of their multi-polar uncertain information. We then provide an algorithm to clearly understand the clustering methodology that we use in our application. Finally, we present a comparative analysis of our research work with existing techniques to prove its applicability and effectiveness.