CLAR POLYNOMIALS OF LARGE BENZENOID SYSTEMS

We discuss the constructions of Clar-like valence structures and the a ssociated Clar polynomials for large benzenoids. We have shown that Cl ar polynomial satisfy a theorem analogous to the Clarke's theorem for the characteristic polynomial of graphs, which allows one to reconstru ct the polynomial of a system from the polynomials associated with qua lified substructures. In the case of Clar's polynomial the substructur es are obtained by deleting individual benzene rings from the consider ed benzenoid, one at a time. This property of Clar polynomial allows o ne to construct the polynomial of larger systems from known Clar's pol ynomials of smaller benzenoids.