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.
Clar structure, Clar polynomial, Sextet polynomial, Buckminsterfullerene, Graph theory
Source Publication Title
Journal of Molecular Structure: THEOCHEM
Link to Publisher's Edition
Shiu, W., Lam, P., & Zhang, H. (2003). Clar and sextet polynomials of buckminsterfullerene. Journal of Molecular Structure: THEOCHEM, 622 (3). https://doi.org/10.1016/S0166-1280(02)00649-8