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A new characterization and a recognition algorithm of Lucas cubes. (English) Zbl 1283.05195

Summary: 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.

MSC:

05C65 Hypergraphs
05C35 Extremal problems in graph theory
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
05C85 Graph algorithms (graph-theoretic aspects)