Student:	Ümmügülsün AKBABA
Supervisor:	Yrd.Doç.Dr.Ali Hikmet DEĞER
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University Turkey

Title of the Thesis:	Imprimitive Action of Minimal Length on the Suborbital Graphs of the Group Γ_0 (N)
Level:	M.Sc.
Acceptance Date:	1/6/2016
Number of Pages:	76
Registration Number:	i3036

Summary:

Major aim of the present thesis is to investigate paths of minimal length of the

suborbital graphs which has rational valuable vertices and to characterize the vertices of

these paths. General aim with the study is to find solution to finding problem of signatures

of discrete groups with circuit lengths on suborbital graphs.

In the first chapter, general informations about the subject were discussed and basic

informations about the concepts of graph theory, hyperbolic geometry and continued

fractions were given respectively with revealing examples.

In the second chapter, the right and left direction connection were established for these

paths of minimal length on the graph F_(u,N) and then using recurrence relations for continued

fractions, some important results were obtained for the vertices of these paths.

Key Words: Farey graphs, Farey sequences, Modular group, Hyperbolic geometry, Graph

theory, Suborbital graphs, Continued fractions, Minimal lengths