Connectivity of Suborbital Graphs for the Congruence Subgroups of the Extended Modular Group

Abstract

Let $ \widehat{\Gamma} $ be the extended modular group acting on $ \widehat{\mathbb{Q}} $ by linear fractional transformation. In this paper, we investigate connectivity of the suborbital graphs $ \widehat{\mathcal{F}}_{u,n} $ for the congruence subgroup $ \widehat{\Gamma}_0(n) $ of $ \widehat{\Gamma} $.