DeLaViña–Waller conjecture on the Wiener index of graphs of order $2d+1$

Let $G$ be a finite connected graph, let $d$ be its diameter, let $W(G)$ denote its Wiener index, and let $C_{2d+1}$ denote the cycle on $2d+1$ vertices. DeLaViña–Waller conjecture. If

$$d\geq 3\quad\text{and}\quad |V(G)|=2d+1,$$

then

$$W(G)\leq W(C_{2d+1}).$$

The conjecture concerns the maximum Wiener index among graphs with prescribed diameter and order. The paper states that it proves the conjecture for relevant classes involving $0,1,2,3$ or $n-4$ cut vertices, while the general problem remains unresolved.