Paths of Minimal Length on Suborbital Graphs with Recurrence Relations

Subject Analysis
Title Paths of Minimal Length on Suborbital Graphs with Recurrence Relations
Author(s) Ali Hikmet Değer and Murat Beşenk and Bahadır Özgür Güler
Keywords Suborbital graphs, Modular group, Minimal lengths, Continued fractions, Recurrence relations.
Abstract

In this paper, we study suborbital graphs for congruence subgroup Γ_0 (N) of the modular group Γ to have vertices of the graph F_(u,N) and hyperbolic paths of minimal length with recurrence relations give rise to a special continued fraction.