Wiener index and graphs, almost half of whose vertices satisfy Šoltés property

Margarita Akhmejanova, Konstantin Olmezov, Aleksei Volostnov +3

The Wiener index $W(G)$ of a connected graph $G$ is a sum of distances between all pairs of vertices of $G$. In 1991, Šoltés formulated the problem of finding all graphs $G$ such t…