Studies on Scientific Developments in Geometry, Algebra, and Applied Mathematics, Ankara, Turkey, 1 - 03 February 2022, pp.67
geometries. [5] developed new concepts on suborbital graph motion. These concepts found an
important place in applications for ﬁnite groups in studies of [4] and [6]. [3] investigated
vertices of suborbital graph Fu,N obtained with an element of Modular group Γ. [1] and [2]
examined that each vertex in the suborbital graph Fu,N has a continued fraction structure. [2]
obtained the value of any vertex on a minimal length path from the type of Fibonacci numbers. In
this study, the vertices of the suborbital graph Fu,N were found as Lucas numbers using the
identity
Fn ∼= √an . Identities related to Fibonacci and Lucas numbers were reached with the help of
identity
pn = (−1)ⁿF₂n ∼= (−1)ⁿ √an Ln where nᵗʰ numerator of the suborbital graph is p