Fibonacci Graphs


Creative Commons License

Gunes A., Delen S., Demirci M., Cevik A. S. , Cangül İ. N.

SYMMETRY-BASEL, vol.12, no.9, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 9
  • Publication Date: 2020
  • Doi Number: 10.3390/sym12091383
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Omega invariant, degree sequence, realizability, Fibonacci number, Fibonacci graph

Abstract

Apart from its applications in Chemistry, Biology, Physics, Social Sciences, Anthropology, etc., there are close relations between graph theory and other areas of Mathematics. Fibonacci numbers are of utmost interest due to their relation with the golden ratio and also due to many applications in different areas from Biology, Architecture, Anatomy to Finance. In this paper, we define Fibonacci graphs as graphs having degree sequence consisting of n consecutive Fibonacci numbers and use the invariant omega to obtain some more information on these graphs. We give the necessary and sufficient conditions for the realizability of a set D of n successive Fibonacci numbers for every n and also list all possible realizations called Fibonacci graphs for 1 <= n <= 4.