## F-INDEX FOR FUZZY GRAPH WITH APPLICATION

## F-INDEX FOR FUZZY GRAPH WITH APPLICATION

*SK R. Islam, M. Pal*

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## Abstract

Di erent 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 de ne 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 nd the most in uenced researcher in that group.

## Keywords

Fuzzy graph, topological indices, Forgotten Topological Index, Forgotten Topological Index for fuzzy graph.