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 > 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.
Published February 1992 , 11 pages