The graphs of congruence subgroups

In this thesis, the action of the group Γo(n/h) on Q^(h) and suborbital graphs arising from this action are investigated. In the first chapter, we give some definitions and theorems requiring for second chapter. In the second chapter, the action of the group Γo(n/h) on Q^(h), the suborbital graphs arising from this action and the conditions being edge in these suborbital graphs are given. After that, the suborbital graphs F_(1,n) for all nϵN , are investigated comprehensively and in these graphs the relation of path connecting to the largest vertices one another and some interesting results contributing to the Number Theory are proved. Finally, the suborbital graphs F_(u,2u+1) and the condition ko=2 of the thorem in [1] are examined.