Suborbital graphs of moduler subgroup Γ^'

In this thesis, the main object is to examine the suborbital graphs arising from the action of the modular subgroup Γ^' on Q∪{∞}. In the first chapter, general informations about the subject are discussed and proofs of some important theorems and conslusions in the literature were given in detail. In the second chapter, the edge and circuit conditions on the suborbital graphs arising from the modular subgroup Γ^' are examined and then the connectedness of the graphs are determined under these conditions.