On suborbital graphs for some Hecke groups Original Research Article

In this paper, we examine some properties of suborbital graphs for the Hecke groups Γ, H(2), and H(3) on Q̂,2Q̂, and 3Q̂, respectively. In addition, we give necessary and sufficient conditions for the suborbital graph G(∞,(u/n)m) to be a forest. Finally, we completely find the number of sides of all the circuits in the suborbital graphs.