Closed-Form Formulas for Zhang-Zhang Polynomials of Hexagonal Graphene Flakes O(k, m, n) with k, m=1-7 and Arbitrary n

We report a closed-form formula for the ZZ polynomials of hexagonal graphene flakes O (k, m, n) with k, m = 1,2,3, ..., 7 and an arbitrary value of n. The discovered formula, ZZ(O(k,m,n),x) = Sigma j=0left perpendicular k.m/2 right perpendicular-1 where clj denotes structural parameters dependent on k and m but independent of n, is obtained by a combinatorial analysis of large families of isostructural hexagonal flakes. The presented results extend the available body of information on the ZZ polynomials of hexagonal graphene flakes O (k, m, n) by a factor of 10. The main reason for presenting these numerical results is to provide the chemical and mathematical communities with reference data necessary for deriving, understanding, and testing general ZZ polynomial formulas valid for a hexagonal flake O (k,m, n) with arbitrary values of the structural parameters k, m, and n.

Automated summary

A closed-form formula for the ZZ polynomials of hexagonal graphene flakes with specific structural parameters is reported, expanding the available information by a factor of 10. The main purpose of presenting these numerical results is to provide reference data for the chemical and mathematical communities to derive, understand, and test general ZZ polynomial formulas for hexagonal flakes with arbitrary parameters.