Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures: prolate rectangles and their generalizations (Q897590)

The Zhang-Zhang polynomial (or the Clar covering polynomial) of a benzenoid system is a counting polynomial of Clar covers, which are structures with aromatic sextets. In this paper, it is shown that the Zhang-Zhang polynomial of a benzenoid obtained by fusing a parallelogram with an arbitrary benzenoid can be computed as a product of the Zhang-Zhang polynomials of both fragments. Also, formal proofs of explicit forms of the Zhang-Zhang polynomial for prolate rectangles and generalized prolate rectangles are given. Furthermore, it is conjectured that the Zhang-Zhang polynomial of a benzenoid obtained by fusing two arbitrary Kekuléan benzenoids can be computed as a product of the Zhang-Zhang polynomials of both fragments.