IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v27y2006i1p233-236.html
   My bibliography  Save this article

On stick number of knots and links

Author

Listed:
  • Elrifai, E.A.

Abstract

The DNA strand is made up of small rigid sticks of sugar, phosphorus, nucleotide proteins and hydrogen bond. A cyclic molecule can be modelled by a sequence of sticks glued end-to-end so that the last one is also glued to the first. Thus we have mathematical stick knots or polygonal knots. This gives rise to some questions: For instance, what is the smallest number of atoms needed to construct a nontrivial knotted molecule? For such stick numbers, Negami gave an upper and lower bound. In the case when a given knot reaches its lower bound in Negami’s inequality, we gave a specific relation between both of its stick and crossing numbers. Hence we conclude that not one of the knots, at least, to 26 crossings can achieve its lower bound. In other words every knotted molecule of atoms up to 26 will have a number of bonds more than the lower bound in Negami’s inequality. Subsequently it is shown that some interesting class of torus knots does not achieve that lower bound in Negami’s inequality.

Suggested Citation

  • Elrifai, E.A., 2006. "On stick number of knots and links," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 233-236.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:233-236
    DOI: 10.1016/j.chaos.2005.03.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790500322X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.03.037?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:233-236. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.