Groupe d’études et de recherche en analyse des décisions


On Clar Graphs


A necessary and sufficient condition is given for the Clar graph and the inner dual of a benzenoid system to be equal. It is shown that k &gt 2 hexagons are not always mutually resonant if they are pairwise resonant. As a consequence, the number of independent sets of k vertices in the Clar graph of a benzenoid system is not always equal to the number of sets of k mutually resonant hexagons. However, this property holds for 3-resonant benzenoid systems and for catacondensed benzenoid systems.

, 11 pages