[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

RETRACTED ARTICLE: On connection number-based topological indices and entropy measures for triangular \(\gamma\)-graphyne network

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

This article was retracted on 06 December 2024

This article has been updated

Abstract

Triangular \(\gamma\)-graphyne has a special carbon–carbon bonding arrangement, which results in outstanding electrical characteristics. It is a potential material for semiconductors and conductors in nanoelectronic devices. The number of vertices at a distance of 2 from a vertex is known as the connection number (CN) of that vertex. In this paper, we computed Zagreb-type indices based on connection numbers. In order to give us a better knowledge of the structural properties of molecules or networks, these indices are calculated. Following the computation of these indices, we investigated their use in computing entropy, providing important new information about the thermodynamic characteristics and complexity of the understudied systems. We used Python language to find the Pearson correlation coefficient between indices and entropy and show its heat map.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

In this article, no data were utilized.

Change history

References

  1. Tutte WT (2001) Graph theory, vol 21. Cambridge University Press, Cambridge

    Google Scholar 

  2. West DB (2001) Introduction to graph theory, vol 2. Prentice Hall, Upper Saddle River

    Google Scholar 

  3. Gutman I, Polansky OE, Gutman I, Polansky OE (1986) Chemical graphs. In: Mathematical Concepts in Organic Chemistry, pp 19–22

  4. Gutman I (2006) Chemical graph theory-the mathematical connection. Adv Quantum Chem 51(5):125–138

    Article  Google Scholar 

  5. García-Domenech R, Gálvez J, de Julián-Ortiz JV, Pogliani L (2008) Some new trends in chemical graph theory. Chem Rev 108(3):1127–1169

    Article  Google Scholar 

  6. Gutman I, Trinajstić N (1972) Graph theory and molecular orbitals. Total pi-electron energy of alternant hydrocarbons. Chem Phys Lett 17(4):535–538

    Article  Google Scholar 

  7. Liu JB, Bao Y, Zheng WT (2022) Analyses of some structural properties on a class of hierarchical scale-free networks. Fractals 30(7):2250136

    Article  Google Scholar 

  8. Liu JB, Bao Y, Zheng WT, Hayat S (2021) Network coherence analysis on a family of nested weighted n-polygon networks. Fractals 29(08):2150260

    Article  Google Scholar 

  9. Liu JB, Zhao J, Min J, Cao J (2019) The Hosoya index of graphs formed by a fractal graph. Fractals 27(08):1950135

    Article  Google Scholar 

  10. Liu JB, Wang C, Wang S, Wei B (2019) Zagreb indices and multiplicative Zagreb indices of Eulerian graphs. Bull Malays Math Sci Soc 42:67–78

    Article  MathSciNet  Google Scholar 

  11. Wiener H (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69(1):17–20

    Article  Google Scholar 

  12. Hayat S, Imran M (2014) Computation of topological indices of certain networks. Appl Math Comput 240(8):213–228

    MathSciNet  Google Scholar 

  13. Javaid M, Ali U, Siddiqui K (2021) Novel connection based Zagreb indices of several wheel-related graphs. Comput J Comb Math 1(7):1–28

    Google Scholar 

  14. Liu JB, Raza Z, Javaid M (2020) Zagreb connection numbers for cellular neural networks. Discret Dyn Nat Soc 20(13):1–8

    MathSciNet  Google Scholar 

  15. Ali MB, Bonyah E, Javaid M (2022) Computing connection-based topological indices of sudoku graphs. J Math 20(5):112–127

    MathSciNet  Google Scholar 

  16. Sattar A, Javaid M, Bonyah E (2022) Computing connection-based topological indices of dendrimers. J Chem 15(23):234–245

    Google Scholar 

  17. Li H, Ma Y, Zhao Y (2022) Total rainbow connection number of some graph operations. Axioms 11(6):254–268

    Article  Google Scholar 

  18. Ullah A, Zaman S, Hamraz A (2023) Zagreb connection topological descriptors and structural property of the triangular chain structures. Phys Scr 98(2):25–38

    Article  Google Scholar 

  19. Rashevsky N (1955) Life, information theory, and topology. Bull Math Biophys 17(4):229–235

    Article  MathSciNet  Google Scholar 

  20. Mowshowitz A (1968) Entropy and the complexity of graphs: II. The information content of digraphs and infinite graphs. Bull Math Biophys 30(5):225–240

    Article  MathSciNet  Google Scholar 

  21. Chen Z, Dehmer M, Shi Y (2014) A note on distance-based graph entropies. Entropy 16(10):5416–5427

    Article  MathSciNet  Google Scholar 

  22. Dehmer M, Mowshowitz A (2011) A history of graph entropy measures. Inf Sci 181(1):57–78

    Article  MathSciNet  Google Scholar 

  23. Nandini GK, Rajan RS, Shantrinal AA, Rajalaxmi TM, Rajasingh I, Balasubramanian K (2020) Topological and thermodynamic entropy measures for COVID-19 pandemic through graph theory. Symmetry 12(12):1992

    Article  Google Scholar 

  24. Feng C, Muhammad MH, Siddiqui MK, Kirmani SAK, Manzoor S, Hanif MF (2022) On entropy measures for molecular structure of remdesivir system and their applications. Int J Quantum Chem 122(18):50–64

    Article  Google Scholar 

  25. Manzoor S, Siddiqui MK, Ahmad S (2020) On entropy measures of molecular graphs using topological indices. Arab J Chem 13(8):6285–6298

    Article  Google Scholar 

  26. Siddiqui MK, Manzoor S, Ahmad S, Kaabar MK (2021) On computation and analysis of entropy measures for crystal structures. Math Probl Eng 2021:1–16

    MathSciNet  Google Scholar 

  27. Mondal S, Das KC (2023) Degree-based graph entropy in structure-property modeling. Entropy 25(7):10–25

    Article  MathSciNet  Google Scholar 

  28. Manzoor S, Siddiqui MK, Ahmad S (2021) On physical analysis of degree-based entropy measures for metal-organic superlattices. Eur Phys J Plus 136(3):1–22

    Article  Google Scholar 

  29. Rashid MA, Ahmad S, Siddiqui MK, Manzoor S, Dhlamini M (2021) An analysis of eccentricity-based invariants for biochemical hypernetworks. Complexity 2021:1–15

    Article  Google Scholar 

  30. Manzoor S, Siddiqui MK, Ahmad S (2021) Degree-based entropy of molecular structure of hyaluronic acid-curcumin conjugates. Eur Phys J Plus 136(1):1–21

    Article  Google Scholar 

  31. Imran M, Manzoor S, Siddiqui MK, Ahmad S, Muhammad MH (2022) On physical analysis of synthesis strategies and entropy measures of dendrimers. Arab J Chem 15(2):1–18

    Article  Google Scholar 

  32. Evans W, Kirkpatrick D, Townsend G (2001) Right-triangulated irregular networks. Algorithmica 30:264–286

    Article  MathSciNet  Google Scholar 

  33. Kreveld MV, Silveira RI (2011) Embedding rivers in triangulated irregular networks with linear programming. Int J Geogr Inf Sci 25(4):615–631

    Article  Google Scholar 

Download references

Funding

This research received no funding.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Muhammad Kamran Siddiqui.

Ethics declarations

Conflict of interest

The authors have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article has been retracted. Please see the retraction notice for more detail:https://doi.org/10.1007/s11227-024-06781-8

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, R., Hanif, M.F., Siddiqui, M.K. et al. RETRACTED ARTICLE: On connection number-based topological indices and entropy measures for triangular \(\gamma\)-graphyne network. J Supercomput 80, 25029–25048 (2024). https://doi.org/10.1007/s11227-024-06398-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-024-06398-x

Keywords

Navigation