Journal of Combinatorial Optimization

, Volume 25, Issue 4, pp 505–522 | Cite as

Structure of Fibonacci cubes: a survey

  • Sandi Klavžar


The Fibonacci cube Γ n is the subgraph of the n-cube induced by the binary strings that contain no two consecutive 1s. These graphs are applicable as interconnection networks and in theoretical chemistry, and lead to the Fibonacci dimension of a graph. In this paper a survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamiltonicity, degree sequence and other enumeration results. Their median nature that leads to a fast recognition algorithm is discussed. The Fibonacci dimension of a graph, studies of graph invariants on Fibonacci cubes, and related classes of graphs are also presented. Along the way some new short proofs are given.


Fibonacci cube Fibonacci number Cartesian product of graphs Median graph Degree sequence Cube polynomial 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Faculty of Natural Sciences and MathematicsUniversity of MariborMariborSlovenia

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