Skip to main content
SpringerLink
Log in

Degree- and irregularity-based molecular descriptors for benzenoid systems

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

Abstract

The study of benzenoid systems has been steadily gaining momentum due to their extensive applications in many emerging fields including nanosciences. Topological descriptors provide a mathematical expression of the molecular structure of chemical compounds and their properties. They serve as efficient and cost-effective tools to theoretically predict the properties of compounds using quantitative structure–activity (QSAR) and structure–property relationship (QSPR) studies. This paper demonstrates the computation of degree-based and irregularity-based topological descriptors using edge-partition techniques for two benzenoid structures. This analysis of degree-based descriptors for these structures can lay the basis for further exploration into benzenoids and their properties.

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

Similar content being viewed by others

References

  1. N. Trinajstic, Chemical Graph Theory (Routledge, Abingdon, 2018)

    Book  Google Scholar 

  2. J. Devillers, A.T. Balaban (eds.), Topological Indices and Related Descriptors in QSAR and QSPAR (CRC Press, Boca Raton, 2000)

    Google Scholar 

  3. F. Emmert-Streib, Statistical Modelling of Molecular Descriptors in QSAR/QSPR (Wiley, Hoboken, 2012)

    Google Scholar 

  4. M.I. Skvortsova, I.I. Baskin, O.L. Slovokhotova, V.A. Palyulin, N.S. Zefirov, Inverse problem in QSAR/QSPR studies for the case of topological indexes characterizing molecular shape (Kier indices). J. Chem. Inf. Comput. Sci. 33(4), 630–634 (1993)

    Article  Google Scholar 

  5. I. Gutman, Degree-based topological indices. Croat. Chem. Acta 86(4), 351–361 (2013)

    Article  Google Scholar 

  6. G. Rücker, C. Rücker, On topological indices, boiling points, and cycloalkanes. J. Chem. Inf. Comput. Sci. 39(5), 788–802 (1999)

    Article  MATH  Google Scholar 

  7. M. Črepnjak, N. Tratnik, P.Ž. Pleteršek, Predicting melting points of hydrocarbons by the Graovac-Pisanski index. Fuller. Nanotub. Carbon Nanostruct. 26(5), 239–245 (2018)

    Article  ADS  Google Scholar 

  8. C. Guan, M. Lu, W. Zeng, D. Yang, D. Han, Prediction of standard enthalpies of formation based on hydrocarbon molecular descriptors and active subspace methodology. Ind. Eng. Chem. Res. 59(10), 4785–4791 (2020)

    Article  Google Scholar 

  9. L.L. Zhou, J.C. Jiang, Y. Pan, Z.R. Wang, A mathematical method for predicting heat of reaction of organic peroxides. J. Loss Prev. Process Ind. 38, 254–259 (2015)

    Article  Google Scholar 

  10. D.H. Rouvray, W. Tatong, Novel applications of topological indices. 3. Prediction of the vapor pressure in polychlorinated biphenyls. Int. J. Environ. Stud. 33(4), 247–257 (1989)

    Article  Google Scholar 

  11. M. Pompe, M. Novic, Prediction of gas-chromatographic retention indices using topological descriptors. J. Chem. Inf. Comput. Sci. 39(1), 59–67 (1999)

    Article  Google Scholar 

  12. F. Liu, Y. Liang, C. Cao, N. Zhou, Theoretical prediction of the Kovat’s retention index for oxygen-containing organic compounds using novel topological indices. Anal. Chim. Acta 594(2), 279–289 (2007)

    Article  Google Scholar 

  13. R. Garcia-Domenech, P. Alarcon-Elbal, G. Bolas, R. Bueno-Marí, F.A. Chordá-Olmos, S.A. Delacour, M.C. Mouriño, A. Vidal, J. Gálvez, Prediction of acute toxicity of organophosphorus pesticides using topological indices. SAR QSAR Environ. Res. 18(7–8), 745–755 (2007)

    Article  Google Scholar 

  14. S.C. Basak, D. Mills, B.D. Gute, G.D. Grunwald, A.T. Balaban, Applications of topological indices in the property/bioactivity/toxicity prediction of chemicals, in Topology in Chemistry, ed. by D. Rouvray, R. Bruce King (Woodhead Publishing, 2002), pp 113–184

  15. P.F. Sheridan, D.B. Adolf, A.V. Lyulin, I. Neelov, G.R. Davies, Computer simulations of hyperbranched polymers: the influence of the Wiener index on the intrinsic viscosity and radius of gyration. J. Chem. Phys. 117(16), 7802–7812 (2002)

    Article  ADS  Google Scholar 

  16. P.V. Khadikar, J. Singh, M. Ingle, Topological estimation of aromatic stabilities of polyacenes and helicenes: modeling of resonance energy and benzene character. J. Math. Chem. 42(3), 433–446 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. J.I. Aihara, Bond resonance energies of polycyclic benzenoid and non-benzenoid hydrocarbons. J. Chem. Soc. Perkin Trans. 2(10), 2185–2195 (1996)

    Article  Google Scholar 

  18. J. Cioslowski, Additive nodal increments for approximate calculation of the total π-electron energy of benzenoid hydrocarbons. Theor. Chim. Acta 68(4), 315–319 (1985)

    Article  Google Scholar 

  19. I. Gutman, S.J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons (Springer, Berlin, 2012)

    MATH  Google Scholar 

  20. J.R. Dias, Handbook of Polycyclic Hydrocarbons. Part A: Benzenoid Hydrocarbons. United States: N. p., 1987. Web

  21. J.N. Murrell, The Theory of the Electronic Spectra of Organic Molecules (Springer, New York, US, 1963). eBook ISBN 978-1-5041-1152-2

  22. D. Lloyd, The Chemistry of Conjugated Cyclic Compounds: To be or Not to be Like Benzene? (Wiley, Hoboken, 1989)

    Google Scholar 

  23. R. Taylor, Electrophilic Aromatic Substitution (Wiley, Chichester, 1990)

    Google Scholar 

  24. L.J. Allamandola, A.G.G.M. Tielens, J.R. Barker, Interstellar polycyclic aromatic hydrocarbons—the infrared emission bands, the excitation/emission mechanism, and the astrophysical implications. Astrophys. J. Suppl. Ser. 71, 733–775 (1989)

    Article  ADS  Google Scholar 

  25. H.I. Abdel-Shafy, M.S. Mansour, A review on polycyclic aromatic hydrocarbons: source, environmental impact, effect on human health and remediation. Egypt. J. Pet. 25(1), 107–123 (2016)

    Article  Google Scholar 

  26. G. Mastrangelo, E. Fadda, V. Marzia, Polycyclic aromatic hydrocarbons and cancer in man. Environ. Health Perspect. 104(11), 1166–1170 (1996)

    Article  Google Scholar 

  27. R. Canton-Vitoria, Y. Sayed-Ahmad-Baraza, M. Pelaez-Fernandez, R. Arenal, C. Bittencourt, C.P. Ewels, N. Tagmatarchis, Functionalization of MoS 2 with 1, 2-dithiolanes: toward donor-acceptor nanohybrids for energy conversion. NPJ 2D Mater. Appl. 1(1), 1–9 (2017)

    Article  Google Scholar 

  28. B.K. Shah, D.C. Neckers, J. Shi, E.W. Forsythe, D. Morton, Anthanthrene derivatives as blue emitting materials for organic light-emitting diode applications. Chem. Mater. 18(3), 603–608 (2006)

    Article  Google Scholar 

  29. J.E. Anthony, Functionalized acenes and heteroacenes for organic electronics. Chem. Rev. 106(12), 5028–5048 (2006)

    Article  Google Scholar 

  30. S.E. Stein, R.L. Brown, pi-Electron properties of large condensed polyaromatic hydrocarbons. J. Am. Chem. Soc. 109(12), 3721–3729 (1987)

    Article  Google Scholar 

  31. M.J.S. Dewar, The Molecular Orbital Theory of Organic Chemistry (McGraw-Hill, New York, 1969)

    Google Scholar 

  32. B.D. Gute, S.C. Basak, Predicting acute toxicity (LC50) of benzene derivatives using theoretical molecular descriptors: a hierarchical QSAR approach. SAR QSAR Environ. Res. 7(1–4), 117–131 (1997)

    Article  Google Scholar 

  33. C. Bertinetto, C. Duce, R. Solaro, K. Héberger, Modeling of the acute toxicity of benzene derivatives by complementary QSAR methods. Match Commun. Math. Comput. Chem. 70(3), 1005–1021 (2013)

    Google Scholar 

  34. J. Wu, W. Pisula, K. Müllen, Graphenes as potential material for electronics. Chem. Rev. 107(3), 718–747 (2007)

    Article  Google Scholar 

  35. Z. Zeng, X. Huang, Z. Yin, H. Li, Y. Chen, H. Li, Q. Zhang, J. Ma, F. Boey, H. Zhang, Fabrication of graphene nanomesh by using an anodic aluminum oxide membrane as a template. Adv. Mater. 24(30), 4138–4142 (2012)

    Article  Google Scholar 

  36. G. Korinth, T. Wellner, K.H. Schaller, H. Drexler, Potential of the octanol-water partition coefficient (log P) to predict the dermal penetration behaviour of amphiphilic compounds in aqueous solutions. Toxicol. Lett. 215(1), 49–53 (2012)

    Article  Google Scholar 

  37. R.S. Braga, P.M.V.B. Barone, D.S. Galvao, Identifying carcinogenic activity of methylated and non-methylated polycyclic aromatic hydrocarbons (PAHs) through electronic and topological indices. Braz. J. Phys. 30(3), 560–568 (2000)

    Article  ADS  Google Scholar 

  38. D.B. West, Introduction to Graph Theory, vol. 2 (Prentice Hall, Upper Saddle River, 1996)

    MATH  Google Scholar 

  39. B. Lučić, N. Trinajstić, B. Zhou, Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons. Chem. Phys. Lett. 475(1–3), 146–148 (2009)

    Article  ADS  Google Scholar 

  40. K.C. Das, M. Dehmer, Comparison between the zeroth-order Randić index and the sum-connectivity index. Appl. Math. Comput. 274, 585–589 (2016)

    MathSciNet  MATH  Google Scholar 

  41. S.C. Basak, G.J. Niemi, G.D. Veith, Predicting properties of molecules using graph invariants. J. Math. Chem. 7(1), 243–272 (1991)

    Article  Google Scholar 

  42. B. Zhao, J. Gan, H. Wu, Redefined Zagreb indices of some nano structures. Appl. Math. Nonlinear Sci. 1(1), 291–300 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  43. M. Eliasi, D. Vukičević, Comparing the multiplicative Zagreb indices. MATCH Commun. Math. Comput. Chem. 69, 765–773 (2013)

    MathSciNet  MATH  Google Scholar 

  44. B. Furtula, A. Graovac, D. Vukičević, Augmented zagreb index. J. Math. Chem. 48(2), 370–380 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  45. D. Vukičević, M. Gašperov, Bond additive modeling 1. Adriatic indices. Croat. Chem. Acta 83(3), 243–260 (2010)

    Google Scholar 

  46. C.K. Gupta, V. Lokesha, S.B. Shwetha, P.S. Ranjini, On the symmetric division deg index of graph. Southeast Asian Bull. Math. 40(1), 59–80 (2016)

    MathSciNet  MATH  Google Scholar 

  47. B. Furtula, I. Gutman, A forgotten topological index. J. Math. Chem. 53(4), 1184–1190 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  48. F.K. Bell, A note on the irregularity of graphs. Linear Algebra Appl. 161, 45–54 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  49. T. Réti, E. Tóth-Laufer, On the construction and comparison of graph irregularity indices. Kragujev. J. Sci. 39, 53–75 (2017)

    Article  Google Scholar 

  50. T. Réti, R. Sharafdini, A. Dregelyi-Kiss, H. Haghbin, Graph irregularity indices used as molecular descriptors in QSPR studies. MATCH Commun. Math. Comput. Chem. 79, 509–524 (2018)

    MathSciNet  Google Scholar 

  51. M. Arockiaraj, J. Clement, K. Balasubramanian, Analytical expressions for topological properties of polycyclic benzenoid networks. J. Chemom. 30(11), 682–697 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  53. A. Miličević, S. Nikolić, N. Trinajstić, On reformulated Zagreb indices. Mol. Divers. 8(4), 393–399 (2004)

    Article  Google Scholar 

  54. V.S. Shegehalli, R. Kanabur, Arithmetic-geometric indices of some class of graph. J. Comput. Math. Sci. 6(4), 194–199 (2015)

    Google Scholar 

  55. A. Usha, P.S. Ranjini, V. Lokesha, Zagreb co-indices, augmented zagreb index, redefined zagreb indices and their polynomials for phenylene and hexagonal squeeze, in Proceedings of International Congress in Honour of Dr. Ravi. P. Agarwal, Uludag University, Bursa, Turkey (2014)

  56. V.S. Shigehalli, R. Kanabur, Computation of new degree-based topological indices of graphene. J. Math. 2016, 4341919 (2016). https://doi.org/10.1155/2016/4341919

    Article  MathSciNet  MATH  Google Scholar 

  57. B. Zhou, N. Trinajstić, On a novel connectivity index. J. Math. Chem. 46(4), 1252–1270 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  58. B. Zhou, N. Trinajstić, On general sum-connectivity index. J. Math. Chem. 47(1), 210–218 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors wish to thank the management of Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam-603110, for their continuous support and encouragement to carry out this research work.

Funding

Funding was provided by National Natural Science Foundation (Grant Nos. 11971142, 11871202, 61673169, 11701176, 11626101, 11601485).

Author information

Authors and Affiliations

  1. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Yu-Ming Chu

  2. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, People’s Republic of China

    Yu-Ming Chu

  3. Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam, Tamil Nadu, 603110, India

    K. Julietraja & P. Venugopal

  4. Department of Mathematics, Comsats University Islamabad, Lahore Campus, Lahore, Pakistan

    Muhammad Kamran Siddiqui

  5. Department of Mathematics, Sri Venkateswara College of Engineering, Sriperumbudur, Tamil Nadu, 602117, India

    Savari Prabhu

Authors
  1. Yu-Ming Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Julietraja
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Venugopal
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad Kamran Siddiqui
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Savari Prabhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Savari Prabhu.

Ethics declarations

Conflict of interest

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chu, YM., Julietraja, K., Venugopal, P. et al. Degree- and irregularity-based molecular descriptors for benzenoid systems. Eur. Phys. J. Plus 136, 78 (2021). https://doi.org/10.1140/epjp/s13360-020-01033-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-01033-z

Search

Navigation