On conjugacy of elliptic elements and circuits in suborbital graphs of congruence subgroups

Abstract

In this paper, we, for the first time, introduce the notion of conjugacy in suborbital graphs. Then we show that the conjugate elliptic elements of the modular group F and of congruence subgroups F 0(p) give rise to conjugate circuits, corresponding to the related elliptic elements, in the Farey graph F and in the suborbital graph F U,p of the action of F 0(P), respectively.