On regular graphs with Šoltés vertices

Nino Bašić, Martin Knor, Riste Škrekovski

Let $W(G)$ be the Wiener index of a graph $G$. We say that a vertex $v\in V(G)$ is a Šoltés vertex in $G$ if $W(G-v)=W(G)$, i.e. the Wiener index does not change if the vertex…