Zhang-Zhang polynomials of regular 3- and 4-tier benzenoid strips

We present compact, closed-form expressions for Zhang-Zhang (ZZ) polynomials of regular 3- and 4-tier benzenoid strips. It is possible to unify the ZZ polynomials of 11 classes of regular 3- and 4-tier benzenoid strips into a single, universal, three-parameter formula (Equation Presented) where Cl ∈ {2,3,4,5,6}, a₀ = 1, a₁ ∈ {0,1,2,3}, and a₂ ∈ {0,1}. The parameters and partition the a₁ and a₂ tiers benzenoid strips into four superfamilies; a₁ and a₂ are constant within a given superfamily and enumerates subsequent benzenoid structures. Our finding provides also a compact and universal expression for the number of Kekulé structures for regular 3- and 4-tier benzenoid strips given by (Equation Presented) These expressions are expected to be readily applicable also to wider regular benzenoid strips.