An investigation of fibonacci trees

• Main Author: Her, Hye Yoon
• Format: text
• Language: English
• Published: Animo Repository 1993
• Subjects: Fibonnaci numbers; Trees (Graph theory)
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16112
• Institution: De La Salle University

A tree is said to be a Fibonacci tree if all the vertices can be labelled with n Fibonacci numbers such that the set of differences of any two adjacent vertices will again consist of the first (n-l) Fibonacci numbers.Fibonacci numbers u1, u2, ... are defined recursively by the equation u1 = u2 = 1 and un = un-1 + un-2 + un-2 for n 3.This study is based on two articles Fibonacci Trees by Koh Khee Meng, Lee Peng Yee and Tan Tay and A Characterization of Fibonacci Trees by Onn Chan and C. C. Chen. This study provides an introduction to the concept of Fibonacci tree. It also gives the proofs of the theorem on the number of Fibonacci trees of order n and a characterization of Fibonacci trees in terms of formal language.