Proof of a conjecture on the Wiener index of Eulerian graphs

The Wiener index of a connected graph is the sum distances between all unordered pairs vertices. A Eulerian if its vertex degrees are even. In Gutman et al. (2014) authors proved that cycle unique maximising among graphs given order. They also conjectured for order n≥26 consisting on n−2 vertices and triangle share with second largest index. conjecture known to hold n≤25 exception six values. this paper we prove conjecture.