Regularni grafi s Šoltésovimi točkami

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 ▫$v$▫ is removed. In 1991, Šoltés posed the problem of identifying all connected graphs ▫$G$▫ with the property that all vertices of ▫$G$▫ are Šoltés vertices. The only such graph known to this day is ▫$C_{11}$▫. As the original problem appears to be too challenging, several relaxations were studied: one may look for graphs with at least ▫$k$▫ Šoltés vertices