Side lengths of pseudoconvex fullerene patches

Graves, Christina; McLoud-Mann, Jennifer

doi:10.26493/1855-3974.231.d5b

Cited by 6 publications

(6 citation statements)

References 8 publications

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“…Next it will be useful to introduce some definitions utilized in [4,5,[14][15][16]. The boundary code of a patch is described by a sequence of 2's and 3's corresponding to the degree of the vertices on the boundary of the patch in cyclic order.…”

Section: Statement Of Resultsmentioning

confidence: 99%

The saturation number of carbon nanocones and nanotubes

Short

2018

Preprint

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Section: Statement Of Resultsmentioning

confidence: 99%

The saturation number of carbon nanocones and nanotubes

Short

2018

Preprint

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“…Let G be the subdivided cube in Figure 23. Let C 1 = (1, 2, 3, 4, 7, 6, 5), 1,5,9,10,14,8) and C 3 = (10, 11,12,13,16,15,14). Then (G; C 1 , C 2 , C 3 ) is an admissible structure.…”

Section: Altans Generalised Altans and Iterated Altansmentioning

confidence: 99%

“…In a previous paper we shifted attention from benzenoids to the more general subcubic planar graphs that we called patches, which generalise the fullerene patches of Graver et al [11,12,13,14,15,16]. In this paper, we similarly generalise coronoids to perforated patches, i.e., to patches with several disjoint holes.…”

Section: Introductionmentioning

confidence: 97%

Coronoids, patches and generalised altans

2016

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In this paper we revisit coronoids, in particular multiple coronoids. We consider a mathematical formalisation of the theory of coronoid hydrocarbons that is solely based on incidence between hexagons of the infinite hexagonal grid in the plane. In parallel, we consider perforated patches, which generalise coronoids: in addition to hexagons, other polygons may also be present. Just as coronoids may be considered as benzenoids with holes, perforated patches are patches with holes. Both cases, coronoids and perforated patches, admit a generalisation of the altan operation that can be performed at several holes simultaneously. A formula for the number of Kekulé structures of a generalised altan can be derived easily if the number of Kekulé structures is known for the original graph. Pauling Bond Orders for generalised altans are also easy to derive from those of the original graph.

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“…Pesudoconvex patches were discussed in detail in [8], and we use the same terminology here. Definition 3.1.…”

Section: Pseudoconvex Patchesmentioning

confidence: 99%