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Journal of Mathematical Chemistry

, Volume 48, Issue 2, pp 401–412 | Cite as

The complexity of Platonic and Archimedean polyhedral links

  • Guang Hu
  • Wen-Yuan Qiu
  • Xiao-Sheng Cheng
  • Shu-Ya Liu
Original Paper

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.

Keywords

Platonic polyhedra Archimedean polyhedra Polyhedral links Knot invariants Complexity measures DNA catenanes 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Guang Hu
    • 1
  • Wen-Yuan Qiu
    • 1
  • Xiao-Sheng Cheng
    • 2
  • Shu-Ya Liu
    • 2
  1. 1.Department of Chemistry, State Key Laboratory of Applied Organic ChemistryLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China

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