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

Correction of a theorem in the Wiener index on fuzzy graphs