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

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