On the role of hypercubes in the resonance graphs of benzenoid graphs

The resonance graph R(B) of a benzenoid graph B has the perfect matchings of B as vertices, two perfect matchings being adjacent13 if their symmetric difference forms the edge set of a hexagon of B. A family P of pair-wise disjoint hexagons of a benzenoid graph B is resonant in B if B.P contains at least one perfect matching, or if B.P is empty. It is proven that there exists a surjective map f15 from the set of hypercubes of R(B) onto the resonant sets of B such that a k-dimensional hypercube is mapped into a resonant set of cardinality k.17

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Khaled Salem, Sandi Klavzar, Ivan Gutman
• Keywords: Benzenoid Graph, DM 2006, Perfect Matching, Resonant Set