Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 5

A classification for bicyclic and tricyclic graphs with respect to Tutte polynomial

Pages
1649–1659
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

We prove some formulas for computing Tutte polynomial of bicyclic and tricyclic graph and finally classify tricyclic graph with respect to Tutte polynomial.**********************************************************************************************************************************************************************************************************************************************************

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The Tutte polynomial of a graph is a polynomial in two variables defined for every simple graph contains information about how the graph is connected.
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Key Findings & Data:The Tutte polynomial of a graph is a polynomial in two variables defined for every simple graph contains information about how the graph is connected.
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Conclusion & Impact:We prove some formulas for computing Tutte polynomial of bicyclic and tricyclic graph and finally classify tricyclic graph with respect to Tutte polynomial.**********************************************************************************************************************************************************************************************************************************************************
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Tutte polynomial · bicyclic · tricyclic graph

Abstract

The Tutte polynomial of a graph is a polynomial in two variables defined for every simple graph contains information about how the graph is connected. We prove some formulas for computing Tutte polynomial of bicyclic and tricyclic graph and finally classify tricyclic graph with respect to Tutte polynomial.**********************************************************************************************************************************************************************************************************************************************************

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Cite This Article

YARAHMADİ, Z., MİR, S. (2022). A classification for bicyclic and tricyclic graphs with respect to Tutte polynomial. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 5, 1649–1659. https://ajindex.com/articles/529562

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References (11)

  1. J.M. Burgos, Singularities in Negamis splitting formula for the Tutte polynomial, Discrete Appl. Math. 237, 65-74, 2018
  2. H.H. Crapo, The Tutte polynomial, Aequationes Math. 3 (3), 211-229, 1969
  3. H. Deng, S. Chen and J. Zhang, The Merrifield-Simmons index in(n, n+1)-graphs, J. Math. Chem. 43, 75-91, 2008
  4. A. Dolati, M. Haghighat, S. Golalizadeh and M. Safari, The smallest Hosoya index of con-nected tricyclic graphs, MATCH Commun. Math. Comput. Chem. 65, 57-70, 2011
  5. S. Li and Z. Zhu, Sharp lower bound for total number of matching of tricyclic graphs, Electron. J. Comb. 17, 15 pages, 2010
  6. S. Ok and T.J. Perrett, Density of real zeros of the Tutte polynomial, Electron. J. Discrete Math. 61, 941-946, 2017
  7. Y.M. Tong, J.B. Liu, Z.Z. Jiang and N.N. Lv, Extreme values of the first general Zagreb index in tricyclic graphs, J. Hefei Univ. Nat. Sci. 1, 4-7, 2010
  8. W.T. Tutte, A contribution to the theory chromatic polynomials, Canad. J.Math. 6, 80-91, 1953
  9. W.T. Tutte, On dichromatic polynomials, J. Combin. Theory 2, 301-320, 1967
  10. W.T. Tutte, On chromatic polynomials and the golden ratio, J. Combin. Theory 9, 289-296, 1970
  11. W.T. Tutte, Graph-polynomials, Adv. Appl. Math. 32, 5-9, 2004.