Abstract
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.
Original language | English |
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Pages (from-to) | 427-442 |
Number of pages | 16 |
Journal | Match |
Volume | 73 |
Issue number | 2 |
Publication status | Published - 2015 |
Externally published | Yes |
ASJC Scopus subject areas
- Chemistry(all)
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics