On Suborbital Graphs with Hyperbolic Geodesics and Entries of Matrices from Some Sequences


DEĞER A. H. , AKBABA Ü. , TUYLU T., Gökcan İ.

17th International Geometry Symposium, Erzincan, Turkey, 19 - 22 June 2019, pp.129

  • Publication Type: Conference Paper / Summary Text
  • City: Erzincan
  • Country: Turkey
  • Page Numbers: pp.129

Abstract

In this study, we investigate the values of the special vertices of the suborbital graph ????,?? and relation between even index terms of famous sequences such as Fibonacci and Lucas. From these relations, we get some new results to have the terms of these sequences. Also we get some connections between the values of these special vertices and matrices consisting of even index terms of these sequences.
Suborbital graphs are formed by imprimitive action, which is the action of a congruence subgroup of the Modular group Γ on the extended rational set Q
^?Q∪{∞}. These graphs are Γ-invariant directed graphs and their vertices are from the set Q^ and their edges are from the set Q
^2 as hyperbolic geodesics in the one type of model of hyperbolic geometry, which is the upper half plane H?{??∈C:????(??)>0}.
We also give some results by using some properties of the suborbital graph ????,?? from [1] with these special sequences.
Keywords: Suborbital Graphs; Modular group; Periodic Continued Fractions; Fibonacci Sequence; Lucas Sequence.