## Abstract

A graph-theoretical definition of Hemdon and Hosoya's Clar structure is given. The Fries Kekulé structure of buckminsterfullerene (C_{60}) with I_{h} symmetry implies that every independent set of hexagon-dual graph (dodecahedron) of C_{60} 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 C_{60}, ξ(C_{60}, χ) = 5χ^{8} + 280χ^{7} + 10χ^{6}, is given, which says that C_{60} possesses a total of 295 Clar structures, and thus corrects a corresponding result recently published. Furthermore, the sextet polynomial of C_{60} is also produced.

Original language | English |
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Pages (from-to) | 239-248 |

Number of pages | 10 |

Journal | Journal of Molecular Structure: THEOCHEM |

Volume | 622 |

Issue number | 3 |

DOIs | |

Publication status | Published - 19 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