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Coronoids, patches and generalised altans

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Abstract

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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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Nino Bašić

  2. Department of Chemistry, University of Sheffield, Sheffield, S3 7HF, UK

    Patrick W. Fowler

  3. FAMNIT, University of Primorska, Glagoljaška 8, 6000, Koper, Slovenia

    Tomaž Pisanski

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  1. Nino Bašić
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  2. Patrick W. Fowler
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  3. Tomaž Pisanski
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Correspondence to Nino Bašić.

Additional information

Research of T. P. and N. B. is supported in part by the ARRS Grant P1-0294.

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Bašić, N., Fowler, P.W. & Pisanski, T. Coronoids, patches and generalised altans. J Math Chem 54, 977–1009 (2016). https://doi.org/10.1007/s10910-016-0599-6

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  • DOI: https://doi.org/10.1007/s10910-016-0599-6

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