C60Br24 as a chemical illustration of graph theoretical independence

Fowler, Patrick W.; Hansen, Peter J.; Rogers, Kevin M.; Fajtlowicz, Siemion

doi:10.1039/a803459a

Cited by 15 publications

(15 citation statements)

References 4 publications

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“…The sole survivor under the simultaneous action of rule (i) and of either version of rule (ii) is the experimental T h isomer, in which the 36 bare carbon centres are arranged as 18 isolated double bonds. 1 The present work is concerned with the extension of these very simple rules to the prediction of the so-far uncharacterised products of bromination of higher fullerenes. A new invariant related to the independence number is required.…”

Section: Introductionmentioning

confidence: 99%

Independent sets and the prediction of addition patterns for higher fullerenes

Fowler¹,

Rogers²,

Somers³

et al. 1999

J. Chem. Soc., Perkin Trans. 2

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Section: Introductionmentioning

confidence: 99%

Independent sets and the prediction of addition patterns for higher fullerenes

Fowler¹,

Rogers²,

Somers³

et al. 1999

J. Chem. Soc., Perkin Trans. 2

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mentioning

confidence: 99%

“…It is one of the handfuls of molecules with this tetrahedral symmetry. [9,10] The very shallow double well potential connecting the two alternate T h structures via an I h barrier will undoubtedly give rise to an interesting fluxional behaviour. Furthermore it is found that the valence orbital structure of the boron buckyball is almost identical to the one in the carbon case.…”

mentioning

confidence: 99%

The boron buckyball has an unexpected Th symmetry

Gopakumar

Nguyen

Ceulemans

2008

Chemical Physics Letters

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The boron buckyball avoids the high symmetry icosahedral cage structure.The previously reported I h symmetric structure is not an energy minimum in the potential energy surface and exhibits a spontaneous symmetry breaking to yield a puckered cage with a rare T h symmetry. The HOMO-LUMO gap is twice as large as the reported value and amounts to 1.94 eV at B3LYP/6-31G(d) level. The valence orbital structure of boron buckyball is identical to the one in the carbon analogue.

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“…15 One of the rules they used was that no sp 3 carbons could be adjacent-that is, the brominated carbons must form an independent set. The paper of Fajtlowicz and Larson 16 suggests a connection between fullerene stability and independence number minimization; Fowler, Daugherty and Myrvold 17 argue that there are better chemical explanations for the observed correlation.…”

Section: Independence In Chemistrymentioning

confidence: 99%

Forcing Independence

Larson¹,

Cleemput²

2013

Croat. Chem. Acta

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Abstract. An independent set in a graph is a set of vertices which are pairwise non-adjacent. An independent set of vertices F is a forcing independent set if there is a unique maximum independent set I such that F ⊆ I. The forcing independence number or forcing number of a maximum independent set I is the cardinality of a minimum forcing set for I. The forcing number f of a graph is the minimum cardinality of the forcing numbers for the maximum independent sets of the graph. The possible values of f are determined and characterized. We investigate connections between these concepts, other structural concepts, and chemical applications. (doi: 10.5562/cca2295)

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C60Br24 as a chemical illustration of graph theoretical independence

Cited by 15 publications

References 4 publications

Independent sets and the prediction of addition patterns for higher fullerenes

Independent sets and the prediction of addition patterns for higher fullerenes

The boron buckyball has an unexpected Th symmetry

Forcing Independence

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