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

Hosoya Polynomial of Graphs Belonging to Twist Knots

Abdulgani Şahin
Bunyamin Şahin
Pages
38–42
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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

In this study, we firstly introduce Hosoya polynomialand we work out the Hosoya polynomials for graphs of twist knots which are one of interesting families of knotsand try to get a generalization for them.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:There is a deep relationship between knot theory and graph theory.
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Key Findings & Data:Graphs are effective tools forstudies into knot theory.
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Conclusion & Impact:In this study, we firstly introduce Hosoya polynomialand we work out the Hosoya polynomials for graphs of twist knots which are one of interesting families of knotsand try to get a generalization for them.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

There is a deep relationship between knot theory and graph theory. Graphs are effective tools forstudies into knot theory. It is possible to switch between the two theories by forming the graphs of knots. Thus, thestudy areas of the two theories meet on a common ground. In this study, we firstly introduce Hosoya polynomialand we work out the Hosoya polynomials for graphs of twist knots which are one of interesting families of knotsand try to get a generalization for them.

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Cite This Article

Şahin, A., Şahin, B. (2022). Hosoya Polynomial of Graphs Belonging to Twist Knots. Turkish Journal of Mathematics and Computer Science, Cilt: 10 - Sayı: 10, 38–42. https://ajindex.com/articles/609187

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References (5)

  1. Deutsch, E., Klavzar, S., Computing Hosoya polynomials of graphs from primary subgraphs, MATCH Communications in Mathematical and in Computer Chemistry, 70(2)(2013), 627–644
  2. Deutsch, E., Klavzar, S., The Hosoya polynomial of distance-regular graphs, Discrete Applied Mathematics, 178(2014), 153–156
  3. Farahani, M.R., On the Schultz polynomial and Hosoya polynomial of circumcoronene series of benzenoid, Journal Applied Mathematics & Informatics, 31(2)(2013), 595–608
  4. Johnson, I., Henrich, A.K., A Interactive Introduction to Knot Theory, Dover Publications, Inc., Mineola, New York, 2017
  5. Deutsch, E., Klavzar, S., Computing Hosoya polynomials of graphs from primary subgraphs, MATCH Communications in Mathematical and in Computer Chemistry, 70(2)(2013), 627–644. 1 [2] Deutsch, E., Klavzar, S., The Hosoya polynomial of distance-regular graphs, Discrete Applied Mathematics, 178(2014), 153–156. 1, 1.1 [3] Farahani, M.R., On the Schultz polynomial and Hosoya polynomial of circumcoronene series of benzenoid, Journal Applied Mathematics & Informatics, 31(2)(2013), 595–608. 1 [4] Johnson, I., Henrich, A.K., A Interactive Introduction to Knot Theory, Dover Publications, Inc., Mineola, New York, 2017. 1.2