Proofs of two conjectures on generalized Fibonacci cubes

  title={Proofs of two conjectures on generalized Fibonacci cubes},
  author={Jianxin Wei and Heping Zhang},
  journal={Eur. J. Comb.},
The structures of bad words
Cube-complements of generalized Fibonacci cubes
Daisy cubes and distance cube polynomial
The self-concatenation of isometric strings is isometric
All good (bad) words consisting of 5 blocks
Generalized Fibonacci cube Qd(f), introduced by Ilić, Klavžar and Rho, is the graph obtained from the hypercube Qd by removing all vertices that contain f as factor. A word f is good if Qd(f) is an
Proof of a conjecture on 2-isometric words
The (non-)existence of perfect codes in Fibonacci cubes
Infinite families of 2-isometric and not 3-isometric binary words


Generalized Fibonacci cubes
Asymptotic number of isometric generalized Fibonacci cubes
The index of a binary word
Fibonacci-like cubes as Z-transformation graphs
The observability of the Fibonacci and the Lucas cubes
Structure of Fibonacci cubes: a survey
A survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamiltonicity, degree sequence and other enumeration results, and their median nature that leads to a fast recognition algorithm is discussed.
Generalized fibonacci cubes are mostly hamiltonian
This work shows that each member of the generalized Fibonacci cubes, which are a new family of graphs that have applications in interconnection topologies, contains a Hamiltonian path.
Recursive fault-tolerance of Fibonacci cube in hypercubes
Structural and enumerative properties of the Fibonacci cubes