Department of Mathematics
A graph-theoretical definition of Herndon 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 thatC60 possesses a total of 295 Clar structures, and thus corrects a corresponding result recently published. Furthermore, the sextet polynomial of C60 is also produced.
Journal of Molecular Structure: THEOCHEM
First Page (page number)
Last Page (page number)
Clar structure, Clar polynomial, Sextet polynomial, Buckminsterfullerene, Graph theory
Shiu, Wai Chee, Peter Che Bor Lam, and Heping Zhang. "Clar and sextet polynomials of buckminsterfullerene." Journal of Molecular Structure: THEOCHEM 622.3 (2003): 239-248.