F-index for fuzzy graph with application

Abstract

Different types of topological index of a graph have many applications and many results are available for crisp graphs. But in many practical applications it is seen that many situations cannot be modeled using crisp graphs. In these cases, to handle such a situation, those topological indices are needed to define in a fuzzy graph. In this article, F-index for fuzzy graphs is introduced and some bounds on F-index are provided for several fuzzy graphs such as path, cycle, star, complete fuzzy graph, etc. In this article, the maximal fuzzy graph is calculated with respect to the F-index for a given vertex set. At the end of this article, a group of researchers are considered and a decision making method is provided by using F-index for fuzzy graph to find the most influenced researcher in that group.