M.Sc. Tezi Görüntüleme

Student:	Hatice ÜNAL
Supervisor:	Prof. Dr. Mehmet AKBAŞ
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University Turkey

Title of the Thesis:	Suborbital Graphs and Fibonacci Numbers
Level:	M.Sc.
Acceptance Date:	12/6/2013
Number of Pages:	70
Registration Number:	i2634

Summary:

In this thesis the main aim is to construct the Fibonacci numbers and generalized Fibonacci numbers by means of the suborbital graphs for the modular group Γ and the group Γ^3, consisting of the cubes of the elements in Γ, and furthermore to give detailed information on the suborbital graphs for the congruence subgroup Γ^0 (n), nϵN.

In the first chapter we give necessary definitions and theorems for the subsequent work.

In the second chapter we studied some basic proberties of the suborbital graphs for the modular group Γ and then by using the disconnectedness of the graph F^3 we arrive at Fibonacci numbers and the generalized Fibonacci numbers. And finally we work out the suborbital graphs for the congruence subgroup Γ^0 (n) , for n natural number. And then we show when the subgraph F_(u,n)^0 is connected and disconnected.

Key Words: Modular group, Fibonacci numbers, Imprimitive action, Suborbital graphs, Connectedness, Disconnectedness