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The complexity of Platonic and Archimedean polyhedral links

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An Erratum to this article was published on 17 September 2010

Abstract

A mathematical methodology for understanding the complexity of Platonic and Archimedean polyhedral links has been developed based on some topological invariants from knot theory. Knot invariants discussed here include crossing number, unknotting number, genus and braid index, which are considered significant in view of DNA nanotechnology. Our results demonstrate that the braid index provides the most structural information; hence, it can be used, among four knot invariants, as the most useful complexity measure. Using such an invariant, it indicates that the complexity of polyhedral links is directed by the number of their building blocks. The research introduces a simple but important concept in the theoretical characterization and analysis of DNA polyhedral catenanes.

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Authors and Affiliations

  1. Department of Chemistry, State Key Laboratory of Applied Organic Chemistry, Lanzhou University, 730000, Lanzhou, People’s Republic of China

    Guang Hu & Wen-Yuan Qiu

  2. School of Mathematics and Statistics, Lanzhou University, 730000, Lanzhou, People’s Republic of China

    Xiao-Sheng Cheng & Shu-Ya Liu

Authors
  1. Guang Hu
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  2. Wen-Yuan Qiu
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  3. Xiao-Sheng Cheng
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  4. Shu-Ya Liu
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Corresponding author

Correspondence to Wen-Yuan Qiu.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s10910-010-9727-x

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Hu, G., Qiu, WY., Cheng, XS. et al. The complexity of Platonic and Archimedean polyhedral links. J Math Chem 48, 401–412 (2010). https://doi.org/10.1007/s10910-010-9682-6

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