Vertices of Paths of Minimal Lengths on Suborbital Graphs

Ali Hikmet Değer

The Modular group $\Gamma$ acts on the set of extended rational numbers $\hat{\mathbb Q}$ transitively. Here, our main purpose is to examine some properties of hyperbolic paths of minimal lengths in the suborbital graphs for $\Gamma$. We characterize all vertices of these hyperbolic paths in the suborbital graphs which are trees.