Clar and sextet polynomials of buckminsterfullerene

Wai Chee Shiu*, Peter Che Bor Lam, Heping Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

14 Citations (Scopus)
12 Downloads (Pure)


A graph-theoretical definition of Hemdon and Hosoya's Clar structure is given. The Fries Kekulé structure of buckminsterfullerene (C60) with Ih symmetry implies that every independent set of hexagon-dual graph (dodecahedron) of C60 corresponds to a sextet pattern; and every maximal independent set to a Clar structure. By proposing the maximal independent set polynomial of a graph and developing its various calculational methods the Clar polynomial of C60, ξ(C60, χ) = 5χ8 + 280χ7 + 10χ6, is given, which says that C60 possesses a total of 295 Clar structures, and thus corrects a corresponding result recently published. Furthermore, the sextet polynomial of C60 is also produced.

Original languageEnglish
Pages (from-to)239-248
Number of pages10
JournalJournal of Molecular Structure: THEOCHEM
Issue number3
Early online date28 Feb 2003
Publication statusPublished - Mar 2003

Scopus Subject Areas

  • Biochemistry
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

User-Defined Keywords

  • Buckminsterfullerene
  • Clar polynomial
  • Clar structure
  • Graph theory
  • Sextet polynomial


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