Correction of a theorem in the Wiener index on fuzzy graphs

TL;DR

This paper corrects a previously published theorem regarding the Wiener index in fuzzy graphs, providing a valid proof and clarifying the mathematical understanding of this concept.

Contribution

It offers the corrected proof of an existing theorem on the Wiener index in fuzzy graphs, addressing previous inaccuracies and enhancing theoretical knowledge.

Findings

The original theorem was incorrect and has now been corrected.

A valid proof of the theorem is provided using the same method as the original author.

The correction clarifies the mathematical properties of the Wiener index in fuzzy graphs.

Abstract

In an article entitled The Counterexample of a theorem in Wiener index of a fuzzy graph and application to illegal immigration networks, we have shown a few examples of incorrect proof of a theorem in the Wiener index. Now, in this article, we will prove it by correcting the desired theorem. We have also used the same method as the author to prove it. There are other methods of proof.