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Journals / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 10 - Sayı: 10

Tutte Polynomial for Graphs of Twist Knots

Abdulgani Şahin
Bunyamin Şahin
Pages
61–66
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Twist knotsare significant class of knots to take into account especially in contact geometry.

📌 3 Key Takeaways

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Objective & Hypothesis:The Tutte polynomial is a two-variable polynomial that is connected by a graph, a matroid or a matrix.The Tutte polynomial has a lot of exciting applications in different areas for example combinatorics, probability,knot theory, algebra, statistical mechanics, computer sciences, chemistry and biology.
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Key Findings & Data:It was indicated by W.
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Conclusion & Impact:Twist knotsare significant class of knots to take into account especially in contact geometry.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The Tutte polynomial is a two-variable polynomial that is connected by a graph, a matroid or a matrix.The Tutte polynomial has a lot of exciting applications in different areas for example combinatorics, probability,knot theory, algebra, statistical mechanics, computer sciences, chemistry and biology. It was indicated by W. T.Tutte. We transport the Tutte polynomial to knot theory. Because each knot have a corresponding graph. Westudy the Tutte polynomial for graphs of twist knots. We find some general forms for the Tutte polynomial ofgraphs belonging to twist knots and the Tutte polynomial of signed graphs belonging to twist knots. Twist knotsare significant class of knots to take into account especially in contact geometry.

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Cite This Article

Şahin, A., Şahin, B. (2022). Tutte Polynomial for Graphs of Twist Knots. Turkish Journal of Mathematics and Computer Science, Cilt: 10 - Sayı: 10, 61–66. https://ajindex.com/articles/609157

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References (4)

  1. Bollobas, B., Modern Graph Theory, Springer Science + Business Media, Inc, New York, 1998
  2. Haggard, G., Pearce, D.J., Royle, G., Computing Tutte polynomials, ACM Transactions on Mathematical Software, 37(3)(2010), Article Number:24
  3. Johnson, I., Henrich, A.K., A Interactive Introduction to Knot Theory, Dover Publications, Inc., Mineola, New York, 2017
  4. Kauffman, L.H., A Tutte polynomial for signed graphs, Discrete Applied Mathematics, 25(1989), 105–127. 1, 1.2