The group Gamma^{0} (N) and relevant suborbital graphs

Abstract

In this study, we investigate the suborbital graphs which are formed by the imprimitive action of the group $\Gamma^{0} (N)$ on the extended rational set and we present some conclusions related with discrete mathematics. In addition, the elements of suborbital graphs are obtained under the act of $\Gamma^{0}(N)$. The vertices are generalized for some special values and are associated with continued fractions. Moreover, the values converged of the right and left vertices are found under certain conditions. Furthermore, the providing of minimal length condition are proved between consecutive vertices.