Proofs of two conjectures on generalized Fibonacci cubes

DOI10.1016/j.ejc.2015.07.018zbMath1321.05165arXiv1501.00378OpenAlexW2964314356WikidataQ113875510 ScholiaQ113875510MaRDI QIDQ499494

Jianxin Wei, Heping Zhang

Publication date: 30 September 2015

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.00378

zbMATH Keywords

embeddable infinite seriesmedian closed subgraphsnon-embeddable infinite series

Mathematics Subject Classification ID

Distance in graphs (05C12) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (15)

A negative answer to a problem on generalized Fibonacci cubes ⋮ Quaternary \(n\)-cubes and isometric words ⋮ The structures of bad words ⋮ The self-concatenation of isometric strings is isometric ⋮ All good (bad) words consisting of 5 blocks ⋮ Infinite families of 2-isometric and not 3-isometric binary words ⋮ Checking whether a word is Hamming-isometric in linear time ⋮ Isometric words based on swap and mismatch distance ⋮ A characterization of non-isometric binary words ⋮ Hypercubes and isometric words based on swap and mismatch distance ⋮ Proof of a conjecture on 2-isometric words ⋮ The (non-)existence of perfect codes in Fibonacci cubes ⋮ Daisy cubes and distance cube polynomial ⋮ Circular embeddability of isometric words ⋮ On \(k\)-ary \(n\)-cubes and isometric words

Cites Work

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• Fast recognition of Fibonacci cubes
• Recursive fault-tolerance of Fibonacci cube in hypercubes
• On median nature and enumerative properties of Fibonacci-like cubes
• Generalized fibonacci cubes are mostly hamiltonian

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