ZZ Polynomials for Isomers of (5,6)-Fullerenes <i>C_n</i> with <i>n</i> = 20–50

Abstract

A compilation of ZZ polynomials (aka Zhang–Zhang polynomials or Clar covering polynomials) for all isomers of small (5,6)-fullerenes Cn with n = 20–50 is presented. The ZZ polynomials concisely summarize the most important topological invariants of the fullerene isomers: the number of Kekulé structures K, the Clar number Cl, the first Herndon number h1, the total number of Clar covers C, and the number of Clar structures. The presented results should be useful as benchmark data for designing algorithms and computer programs aiming at topological analysis of fullerenes and at generation of resonance structures for valence-bond quantum-chemical calculations.

Keywords

• fullerene isomers
• ZZ polynomials
• Clar covers
• Clar covering polynomials
• Kekulé counts and Clar numbers of fullerenes