Ph.D. Tezi Görüntüleme

Student:	Ali Hikmet DEĞER
Supervisor:	Prof. Dr. Mehmet AKBAŞ
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University Turkey

Title of the Thesis:	Curves Of Minimal Length With Q ̂ Vertex On Suborbital Graphs Of The Group Γ_0 (n)
Level:	Ph.D.
Acceptance Date:	18/11/2011
Number of Pages:	80
Registration Number:	Di874

Summary:

In the first chapter, general informations about the subject were discussed and proofs of some important theorems and conclusions in the literature were given detailed. In addition, fundemental informations on concepts of “continued fractions”, “hyperbolic geometry” and “graph theory” were given with revealing examples.

In the second chapter, firstly, to draw the Farey graph with the computer program, required program codes and graphical user interface were given. Then, to have hyperbolic paths of minimal lengths, some important results about suborbital graphs for congruence subgroup Γ_0 (n) of the Modular group Γ were given.

Key Words: Farey graphs, Farey sequences, Modular group, Hyperbolic geometry, Graph theory, Suborbital graphs, Continued fractions