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Linear Recognition and Embedding of Fibonacci Cubes

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Abstract

Fibonacci strings are binary strings that contain no two consecutive 1s. The Fibonacci cube Γ h is the subgraph of the h-cube induced by the Fibonacci strings. These graphs are applicable as interconnection networks and in theoretical chemistry, and lead to the Fibonacci dimension of a graph. We derive a new characterization of Fibonacci cubes. The characterization is the basis for an algorithm which recognizes these graphs in linear time. Moreover, a graph which was recognized as a Fibonacci cube can be embedded into a hypercube using Fibonacci strings within the same time bound.

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Acknowledgements

The work is supported by the Ministry of Science of Slovenia under the grant 0101-P-297.

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  1. Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia

    Aleksander Vesel

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  1. Aleksander Vesel
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Correspondence to Aleksander Vesel.

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Vesel, A. Linear Recognition and Embedding of Fibonacci Cubes. Algorithmica 71, 1021–1034 (2015). https://doi.org/10.1007/s00453-013-9839-3

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  • DOI: https://doi.org/10.1007/s00453-013-9839-3

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