Classification and generation of nanocones

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Nanocones are carbon networks that can be modeled as infinite cubic plane graphs with 1≤p≤5 pentagons and all the other faces hexagons. In this paper, we give a short proof of the fact that nanocones fall into eight classes when classified according to isomorphism up to a finite region, and describe a finer classification taking the localization of the pentagons into account. For this finer classification, we also describe an efficient algorithm to enumerate all non-equivalent nanocone representatives for a given parameter set, and give results of an implementation of the algorithm. © 2011 Elsevier B.V. All rights reserved.

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Brinkmann, G., & Van Cleemput, N. (2011). Classification and generation of nanocones. Discrete Applied Mathematics, 159(15), 1528–1539.

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