Ph.D. Tezi Görüntüleme

      In this thesis, the main object is to examine the relationships between the lengths of circuits of suborbital graphs arising from the action of the subgroup Γ^3≔{(■(a&b@c&d))∈Γ:ab+cd≡0 (mod 3)} of modular group Γ and Hecke group G_5 generated by (■(0&-1@1&0))"and" (■(1&λ@0&1)) on Q∪{∞} and Q[λ]∪{∞} respectively and orders of generating elliptic elements of these groups. And furthermore connectedness of suborbital graphs for the group Γ^3 is presented.

      In Chapter 2, two different problems are discussed. Firstly, suborbital graphs arising from modular subgroup Γ^3 are examined. And then edge and circuit conditions on these graphs are determined and the connectedness of graphs are examined under these conditions. Secondly, suborbital graphs arising from Hecke group G_5 are examined and edge conditions of these graphs are obtained under some certain conditions.