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) |