Document Type

Journal Article

Department/Unit

Department of Mathematics

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.

Publication Year

2003

Journal Title

Journal of Molecular Structure: THEOCHEM

Volume number

622

Issue number

3

Publisher

Elsevier

First Page (page number)

239

Last Page (page number)

248

Referreed

1

DOI

10.1016/S0166-1280(02)00649-8

ISSN (print)

01661280

Keywords

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

Included in

Mathematics Commons

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