Knor–Škrekovski–Tepeh conjecture on maximum-Wiener-index orientations of trees

Let $T$ be a tree, and let $D$ be an orientation of $T$. The Wiener index $W(D)$ is the sum of the directed distances over all ordered pairs of vertices, where the distance is the length of a shortest directed path when one exists and is $0$ otherwise.

Knor–Škrekovski–Tepeh conjecture. If $D$ maximises $W(D)$ among all orientations of $T$, then there exists a vertex $v$ in $D$ such that for every vertex $u$ there exists either a $(u,v)$-path or a $(v,u)$-path in $D$.

The conjecture concerns the structure of orientations of trees with maximum Wiener index. The supplied text does not state whether it has been proved or disproved.