Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

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.

Keywords

Clar structure, Clar polynomial, Sextet polynomial, Buckminsterfullerene, Graph theory

Publication Date

2003

Source Publication Title

Journal of Molecular Structure: THEOCHEM

Volume

622

Issue

3

Start Page

239

End Page

248

Publisher

Elsevier

Peer Reviewed

1

DOI

10.1016/S0166-1280(02)00649-8

Link to Publisher's Edition

http://dx.doi.org/10.1016/S0166-1280(02)00649-8

ISSN (print)

01661280

Included in

Mathematics Commons

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