Skip to main content
SpringerLink
Log in

On degree-based topological descriptors of graphyne and graphdiyne nanoribbons

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

The molecular structure topological descriptors are numeric invariants associated with a given molecular graph and exhibit the underlying molecular topology of the given molecular graph. They play a very important role in predicting certain physico-chemical properties and are useful in QSAR/QSPR analysis. In this article, we demonstrated a formula for calculating any degree-based topological index for graphene and graphdiyne nanoribbons. This finding interpolates other distinguished findings in this field of study. We also provide precise values for a number of well-known degree-based molecular topological indices for graphene and graphdiyne nanoribbons. A graph-theoretical analysis and comparison are also provided to show the vital importance and validation of the obtained results.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data Availability Statement

All data generated or analyzed during this study are included in this article.

References

  1. A. Ahmad, On the degree based topological indices of benzene ring embedded in P-type-surface in 2D network. Hacet. J. Math. Stat. 47(1), 9–18 (2018)

    MathSciNet  MATH  Google Scholar 

  2. A. Ahmad, Computation of certain topological properties of honeycomb networks and Graphene. Disc. Math. Ago. Appl. 9(5), 35–55 (2017)

    Google Scholar 

  3. M. Arockiaraj, S. Klavžar, S. Mushtaq, K. Balasubramanian, Distance-based topological indices of nanosheets, nanotubes and nanotori of \(SiO_2\). J. Math. Chem. 57(1), 343–369 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Arockiaraj, S. Klavžar, S. Mushtaq, K. Balasubramanian, Topological indices of the subdivision of a family of partial cubes and computation of SiO2 related structures. J. Math. Chem. 57, 1868–1883 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Gao, M.R. Farahani, M. Imran, M.R.R. Kanna, Distance-based topological polynomials and indices of friendship graphs. Springer Plus 5, 15–23 (2016)

    Article  Google Scholar 

  6. K.H. Rosen, Discrete Mathematics and Its Applications, 7th edn. (McGraw-Hill, NewYork, 2012)

    Google Scholar 

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

    Article  Google Scholar 

  8. S. Akhter, W. Gao, M. Imran, M.R. Farahani, On topological indices of honeycomb networks and graphene networks. Hacet. J. Math. Stat. 47(1), 19–35 (2018)

    MathSciNet  MATH  Google Scholar 

  9. M.F. Nadeem, S. Zafar, Z. Zahid, On topological properties of the line graphs of subdivision graphs of certain nanostructures. Appl. Math. Comput. 273, 125–130 (2016)

    MathSciNet  MATH  Google Scholar 

  10. I. Gutman, Ž Tomović, Relation between distance-based topological indices. J. Chem. Inf. Comput. Sci. 40(6), 1333–1336 (2000)

    Article  Google Scholar 

  11. M. Mirzargar, A.R. Ashraf, Some distance-based topological indices of a non-commuting graph. Hacet. J. Math. Stat. 41(4), 515–526 (2012)

    MathSciNet  MATH  Google Scholar 

  12. K. Elahi, A. Ahmad, R. Hasni, Construction algorithm for zero divisor graphs of finite commutative rings and their vertex-based eccentric topological indices. Mathematics 6(12), 301–312 (2018)

    Article  MATH  Google Scholar 

  13. M. Ghorbani, M.A. Hosseinzadeh, A new version of Zagreb indices. Filomat 26, 93–100 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Vukičević, A. Graovac, Note on the comparison of the first and second normalized Zagreb eccentricity indices. Acta Chim. Slov. 57, 524–528 (2010)

    Google Scholar 

  15. X. Zhang, X. Wu, S. Akhter, M.K. Jamil, J.B. Liu, M.R. Farahani, Edge-version atom-bond connectivity and geometric arithmetic indices of generalized bridge molecular graphs. Symmetry 10(12), 751–786 (2018)

    Article  ADS  MATH  Google Scholar 

  16. X. Zhang, H.M. Awais, M. Javaid, M.K. Siddiqui, Multiplicative Zagreb indices of molecular graphs. J. Chem. 2019, 1–19 (2019)

    Article  Google Scholar 

  17. Xiujun Zhang, Abdul Rauf, Muhammad Ishtiaq, Muhammad Kamran Siddiqui, Mehwish Hussain Muhammad, On degree based topological properties of two carbon nanotubes. Polycyclic Aromat. Compd. 10, 22–35 (2020)

    Google Scholar 

  18. M.F. Nadeem, M. Imran, H.M.A. Siddiqui, M. Azeem, A. Khalil, Y. Ali, Topological aspects of metal-organic structure with the help of underlying networks. Arab. J. Chem. 14(6), 103–123 (2021)

    Article  Google Scholar 

  19. A.N. Koam, A. Ahmad, M.F. Nadeem, Comparative study of valency-based topological descriptor for Hexagon star network. Comput. Syst. Sci. Eng. 36(2), 293–306 (2021)

    Article  Google Scholar 

  20. M.R. Farahani, S. Ediz, M. Imran, On novel harmonic indices of certain nanotubes. Int. J. Adv. Biotechnol. Res. 8(4), 277–282 (2017)

    Google Scholar 

  21. Z. Ahmad, M. Naseem, M. Naseem, M.K. Jamil, M.F. Nadeem, S. Wang, Eccentric connectivity indices of titania nanotubes TiO2 [m; n]. Eurasian Chem. Commun. 2(6), 712–721 (2020)

    Article  Google Scholar 

  22. S. Wang, M.R. Farahani, M.R.R. Kanna, M.K. Jamil, R.P. Kumar, The wiener index and the Hosoya polynomial of the Jahangir graphs. Appl. Comput. Math. 5(3), 138–141 (2016)

    Article  Google Scholar 

  23. X. Zhang, H. Jiang, J.B. Liu, Z. Shao, The cartesian product and join graphs on edge-version atom-bond connectivity and geometric arithmetic indices. Molecules 23(7), 1–17 (2018)

    Article  Google Scholar 

  24. X. Zhang, M. Naeem, A.Q. Baig, M.A. Zahid, Study of hardness of superhard crystals by topological indices. J. Chem. 10, 7–20 (2021)

    Google Scholar 

  25. X. Zhang, M.K. Siddiqui, S. Javed, L. Sherin, F. Kausar, M.H. Muhammad, Physical analysis of heat for formation and entropy of Ceria Oxide using topological indices. Comb. Chem. High Throughput Screen. 25(3), 441–450 (2022)

    Article  Google Scholar 

  26. M.K. Siddiqui, M. Naeem, N.A. Rahman, M. Imran, Computing topological indices of certain networks. J. Optoelectron. Adv. Mater. 18, 884–892 (2016)

    Google Scholar 

  27. M.K. Siddiqui, Y.M. Chu, M. Nasir, M.F. Nadeem, M.F. Hanif, On topological descriptors of ceria oxide and their applications. Main Group Met. Chem. 44(1), 103–116 (2021)

    Article  Google Scholar 

  28. Z. Ahmad, Z.S. Mufti, M.F. Nadeem, H. Shaker, H.M.A. Siddiqui, Theoretical study of energy, inertia and nullity of phenylene and anthracene. Open Chem. 19(1), 541–547 (2021)

    Article  Google Scholar 

  29. T. Vetrik, Degree-based topological indices of hexagonal nanotubes. J. Appl. Math. Comput. 58(1), 111–124 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  30. A. Ahmad, Topological properties of Sodium chloride. UPB Sci. Bull. Series B 82(1), 35–46 (2020)

    Google Scholar 

  31. M. Ghorbani, A. Khaki, A note on the fourth version of geometric-arithmetic index. Optoelectron. Adv. Mater. Rapid Commum. 4(12), 2212–2215 (2010)

    Google Scholar 

  32. T. Vetrik, Degree-based topological indices of TUC4C8(S) nanotubes. UPB Sci. Bull. Series B 81(4), 187–196 (2019)

    Google Scholar 

  33. Y. Gao, S. Ediz, M.R. Farahani, M. Imran, On the second harmonic index of titania nanotubes. Drug Des. Int. Prop. Int. J. 1(1), 11–21 (2018)

    Google Scholar 

  34. M.O. Albertson, The irregularity of a graph. Ars Combin. 46, 219–225 (1997)

    MathSciNet  MATH  Google Scholar 

  35. M.M. Haley, S.C. Brand, J.J. Pak, Carbon networks based on dehydrobenzoannulenes: synthesis of graphdiyne substructures. Angew. Chem. Int. Ed. 36, 836–838 (1997)

    Article  Google Scholar 

  36. M. Arockiaraj, J. Clement, N. Tratnik, S. Mushtaq, K. Balasubramanian, Weighted Mostar indices as measures of molecular peripheral shapes with applications to graphene, graphyne and graphdiyne nanoribbons. SAR QSAR Environ. Res. 31(3), 187–208 (2020)

    Article  Google Scholar 

Download references

Funding

This research is supported by the UAEU-AUA (Asian Universities Alliance) grants of United Arab Emirates University (UAEU) via Grant No. G00003461.

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates

    Muhammad Imran

  2. College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia

    Ali Ahmad

  3. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan

    Muhammad Kamran Siddiqui

Authors
  1. Muhammad Imran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Kamran Siddiqui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Imran.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Imran, M., Ahmad, A. & Siddiqui, M.K. On degree-based topological descriptors of graphyne and graphdiyne nanoribbons. Eur. Phys. J. Plus 137, 1372 (2022). https://doi.org/10.1140/epjp/s13360-022-03514-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-03514-9

Search

Navigation