Gökcan, İbrahimDeǧer, Ali HikmetÇaglayan, Ümmügülsün2024-12-092024-12-0920241304-7191https://doi.org/10.14744/sigma.2024.00112https://hdl.handle.net/11494/5141In this study, we investigate the vertices arising from the action of a suborbital graph, in terms of continued fractions, matrix, and recurrence relations. Using the approximation of Fibonacci sequence by the Binet formula, we demonstrate that the vertices of the suborbital graph are related to Lucas numbers. Then, we provide new identities and approximations regarding Fibonacci, Lucas, Pell, and Pell-Lucas numbers.eninfo:eu-repo/semantics/openAccessContinued FractionGeneralized Fibonacci NumbersModular GroupArticle4251439144710.14744/sigma.2024.00112Q3Q3