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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Folding of Trefoil Knot and its Graph

M. El-Ghoul, A. I. Elrokh and M. M.A. Shamiri

Abstract

In this study, we introduce the effect of the folding, conditional folding, retraction and conditional retraction on trefoil knot and its graph. We introduce the sheeted trefoil knot and the folding and retraction of this type and present the limit of foldings. We study how to obtain the types of link graph by adjacency matrix for any number of vertices and how to calculate Jones polynomial for this by its connection with Tutte polynomial. The link graph which represents a trefoil knot applied as an example.

Journal of Mathematics and Statistics
Volume 2 No. 2, 2006, 378-385

DOI: https://doi.org/10.3844/jmssp.2006.378.385

Submitted On: 22 June 2006 Published On: 30 June 2006

How to Cite: El-Ghoul, M., Elrokh, A. I. & Shamiri, M. M. (2006). Folding of Trefoil Knot and its Graph. Journal of Mathematics and Statistics, 2(2), 378-385. https://doi.org/10.3844/jmssp.2006.378.385

Open AccessCopyright: © 2006 M. El-Ghoul, A. I. Elrokh and M. M.A. Shamiri. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Folding
  • retraction
  • knot
  • link graph
  • trefoil knot