A Generalization of the Suborbital Graphs Generating Fibonacci Numbers for the Subgroup Γ3

The Modular group Gamma is the most well-known discrete group with many applications. This work investigates some subgraphs of the subgroup Gamma(3), defined by {((c d) (a b)) is an element of Gamma : ab + cd 0 (mod 3)} In [1], the subgraph F-1,F-1 of the subgroup Gamma(3) subset of Gamma is studied, and Fibonacci numbers are obtained by means of the subgraph of F-1,F-1. In this paper, we give a generalization of the subgraphs generating Fibonacci numbers for the subgroup Gamma(3) and some subgraphs having special conditions.