Special vertices of trees on suborbital graphs with recurrence relations of continued fractions

The main purpose of this thesis; from the notion of minimal length path (trees) of suborbital graph F_(u,N), is to examine the vertices in this path by associating them with continued fraction structures. The thesis consists of two parts. In the first part, the preliminary information to be used in the study is under the headings of Fibonacci, Lucas, Pell, Pell-Lucas number sequences, generating functions, continued fractions, recurrence relations, Γ modular group, Farey, F_(u,N), G_(u,N) graphs are given. In the second part, after obtaining the transformation that gives the vertices on the minimal-length path in the F_(u,N) suborbital graph with the k_i values on u^2+(-1)^i k_i u+1≡0 (modN),i=1,2, 1Keyword: Graflar = Graphs ; Lucas sayıları = Lucas numbers ; Pell denklemi = Pell equation ; Sürekli kesirler = Continued fractions ; Üretim fonksiyonları = Production functions