Imprimitive action of minimal length on the suborbital graphs of the group Γo(N)

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.