Relationships with the Fibonacci Numbers and the Special Vertices of the Suborbital Graphs
Öz
Using general ideas in the study of (Sims, 1967), suborbital graphs produced by imprimitive action on rational projective line of the modular group were examined. Properties of Farey graph were extended to suborbital graphs , where and (Jones et al., 1991). In our previous study, trees which are subgraphs of the suborbital graphs consisting of the orbits in block of were examined. Relationships of continued fractions with vertices of paths of minimal length on the subgraphs were established and value of the farthest vertex which a vertex can be bound on this path of the suborbital graph was found (Deger et al., 2011). In the present study, using structure of continued fractions, relationships of values of these type of vertices with Fibonacci numbers in special cases were investigated. As a most important result, equation was found, where and value of Fibonacci number sequence for all natural number is as . In addition, terms of Fibonacci sequence and were obtained by using this matrix.
Anahtar Kelimeler
Suborbital Graphs,Fibonacci Numbers,Minimal Length,Continued Fractions
Kaynakça
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