Clar Polynomials of Large Benzenoid Systems^†

We discuss the constructions of Clar-like valence structures and the associated Clar polynomials for large benzenoids. We have shown that Clar polynomial satisfy a theorem analogous to the Clarke's theorem for the characteristic polynomial of graphs, which allows one to reconstruct the polynomial of a system from the polynomials associated with qualified substructures. In the case of Clar's polynomial the substructures are obtained by deleting individual benzene rings from the considered benzenoid, one at a time. This property of Clar polynomial allows one to construct the polynomial of larger systems from known Clar's polynomials of smaller benzenoids.