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**1 - 2**of**2**### On the role of hypercubes in . . .

- DISCRETE MATHEMATICS
, 2006

"... The resonance graph R(B) of a benzenoid graph B has the perfect matchings of B as vertices, two perfect matchings being adjacent 13 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 a ..."

Abstract
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The resonance graph R(B) of a benzenoid graph B has the perfect matchings of B as vertices, two perfect matchings being adjacent 13 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 f 15 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.