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



Abstract. Modular group is one of the most well-known discrete group with many applications. This
work investigates some subgraphs of the subgroup Γ3 of the modular group Γ defined by
f( a b c d ) 2 Γ : ab + cd ≡ 0 (mod 3)g
In previous study mentioned in [1], the subgraph F1;1 of the subgroup Γ3 is only studied, and Fibonacci
numbers are obtained by the subgraph F1;1. In this paper, we give a generalization of the subgraphs
generating Fibonacci numbers for the subgroup Γ3 and some subgraphs providing special conditions.


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