Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651201 | Discrete Mathematics | 2006 | 6 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Khaled Salem, Sandi Klavžar, Ivan Gutman,