Clar and sextet polynomials of buckminsterfullerene

Wai Chee Shiu; Peter Che Bor Lam; Heping Zhang

doi:10.1016/S0166-1280(02)00649-8

Clar and sextet polynomials of buckminsterfullerene

Wai Chee Shiu^*, Peter Che Bor Lam, Heping Zhang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

14 Citations (Scopus)

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Abstract

A graph-theoretical definition of Hemdon and Hosoya's Clar structure is given. The Fries Kekulé structure of buckminsterfullerene (C₆₀) with I_h 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 that C₆₀ possesses a total of 295 Clar structures, and thus corrects a corresponding result recently published. Furthermore, the sextet polynomial of C₆₀ is also produced.

Original language	English
Pages (from-to)	239-248
Number of pages	10
Journal	Journal of Molecular Structure: THEOCHEM
Volume	622
Issue number	3
Early online date	28 Feb 2003
DOIs	https://doi.org/10.1016/S0166-1280(02)00649-8
Publication status	Published - 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

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10.1016/S0166-1280(02)00649-8

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title = "Clar and sextet polynomials of buckminsterfullerene",

abstract = "A graph-theoretical definition of Hemdon and Hosoya's Clar structure is given. The Fries Kekul{\'e} 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 that C60 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 = "Buckminsterfullerene, Clar polynomial, Clar structure, Graph theory, Sextet polynomial",

author = "Shiu, {Wai Chee} and Lam, {Peter Che Bor} and Heping Zhang",

note = "Funding Information: This work is partially supported by FRG, Hong Kong Baptist University; National Natural Science Foundation of China and TRAPOYT.",

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T1 - Clar and sextet polynomials of buckminsterfullerene

AU - Shiu, Wai Chee

AU - Lam, Peter Che Bor

AU - Zhang, Heping

N1 - Funding Information: This work is partially supported by FRG, Hong Kong Baptist University; National Natural Science Foundation of China and TRAPOYT.

PY - 2003/3

Y1 - 2003/3

N2 - A graph-theoretical definition of Hemdon 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 that C60 possesses a total of 295 Clar structures, and thus corrects a corresponding result recently published. Furthermore, the sextet polynomial of C60 is also produced.

AB - A graph-theoretical definition of Hemdon 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 that C60 possesses a total of 295 Clar structures, and thus corrects a corresponding result recently published. Furthermore, the sextet polynomial of C60 is also produced.

KW - Buckminsterfullerene

KW - Clar polynomial

KW - Clar structure

KW - Graph theory

KW - Sextet polynomial

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VL - 622

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JO - Journal of Molecular Structure: THEOCHEM

JF - Journal of Molecular Structure: THEOCHEM

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ER -

Clar and sextet polynomials of buckminsterfullerene

Abstract

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