Discrete Mathematics & Theoretical Computer Science, Vol 15, No 3 (2013)

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A new characterization and a recognition algorithm of Lucas cubes

Andrej Taranenko


Fibonacci and Lucas cubes are induced subgraphs of hypercubes obtained by excluding certain binary strings from the vertex set. They appear as models for interconnection networks, as well as in chemistry. We derive a characterization of Lucas cubes that is based on a peripheral expansion of a unique convex subgraph of an appropriate Fibonacci cube. This serves as the foundation for a recognition algorithm of Lucas cubes that runs in linear time.

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