Closed-Form Formulas for the Zhang-Zhang Polynomials of Benzenoid Structures: Chevrons and Generalized Chevrons

Abstract

Closed-form, general formulas for the Zhang-Zhang (ZZ) polynomials for two important classes of benzenoid structures, chevrons Ch(k, m, n) and generalized chevrons Ch(k, m, n(1), n(2)), are formally derived. The derivations rely on a new and important theorem, which states that the ZZ polynomial of two fused parallelograms can be represented as the product of the ZZ polynomials of the two separated fragments. This theoretical result seems to play an important role in the theory of pericondensed benzenoids and may prove useful for the process of discovering closed-form formulas of Zhang-Zhang polynomials of for a wide class of benzenoid structures.