Relations generated by special vertices of minimal lenghts paths on suborbital graphs

The main goal in this thesis is to generate new connections using concepts related to the values of the vertices of the minimal length paths of the suborbital graphs. The overall goal with this study is to achieve new results with these connections and try to create new application areas. In the first chapter, general informations about the subject were discussed and basic informations about the concepts of hyperbolic geometry, special number sequences, continued fractions and graph theory were given respectively. In addition, some important theorems and conclusions in the literature were included. In the second chapter, Some results were obtained by using recurrence relations of continued fractions for vertex values in minimal length paths on the F_(u,N). Then, on graph F_1,2, minimal length paths were transferred to the Poincare disk using special vertex values.