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On the construction of some bioconjugate networks and their structural modeling via irregularity topological indices

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Abstract

Bioconjugate networks refer to networks that are formed by connecting different molecules or particles (such as proteins, enzymes, or nanoparticles) through covalent or non-covalent interactions. These networks are often used in various biological and biomedical applications, such as drug delivery, biosensors, and tissue engineering. The specific properties and behavior of these networks depend on the types of molecules used and the nature of their interactions, which can be studied using various computational and experimental techniques. Farnesyl and geranyl groups are types of isoprenoid chains that are commonly found in various biological molecules such as proteins, lipids, and pigments. The addition of these groups to penicillin molecules may alter their physical and chemical properties, such as solubility, stability, and bioavailability. To gain a better understanding of the structure–property relationships of these antibiotics, this study computes various irregularity indices such as the Albertson index, irregularity index, total irregularity index, Randić irregularity index, and other degree-based indices for two types of sensitive bonds of bioconjugate networks. Numerical results and graphical representations are used to illustrate these findings. The obtained results provide valuable insights into the structure–property relationships of penicillins, which will aid in a better understanding of their behavior and developing more effective antibiotics.

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References

  1. M. Naeem et al., Degree-based topological indices of geranyl and farnesyl penicillin G bioconjugate structure. J Eur. Phys. J. Pluss 137(3), 1–16 (2022)

    Google Scholar 

  2. S. Zaman et al., Maximum H-index of bipartite network with some given parameters. AIMS Math. 6(5), 5165–5175 (2021)

    MathSciNet  MATH  Google Scholar 

  3. J.-B. Liu, Y.A.N. Bao, W.-T. Zheng, Analyses of some structural properties on a class of hierarchical scale-free networks. Fractals 30(07), 2250136 (2022)

    MATH  ADS  Google Scholar 

  4. J.-B. Liu et al., On topological properties of planar octahedron networks. Polycycl. Aromat. Compd. 43(1), 755–771 (2023)

    Google Scholar 

  5. S. Zaman et al., QSPR analysis of some novel drugs used in blood cancer treatment via degree based topological indices and regression models. Polycycl. Aromat. Compd. (2023). https://doi.org/10.1080/10406638.2023.2217990

    Article  Google Scholar 

  6. S. Zaman, A. Ullah, A. Shafaqat, Structural modeling and topological characterization of three kinds of dendrimer networks. Eur. Phys. J. E Soft. Matter. 46(5), 36 (2023)

    Google Scholar 

  7. S. Zaman et al., Three-dimensional structural modelling and characterization of sodalite material network concerning the irregularity topological indices. J. Math. 2023, 1–9 (2023)

    MathSciNet  Google Scholar 

  8. S. Zaman et al., On the topological descriptors and structural analysis of cerium oxide nanostructures. Chem. Pap. 77(5), 2917–2922 (2023)

    Google Scholar 

  9. S. Zaman et al., Mathematical analysis and molecular descriptors of two novel metal–organic models with chemical applications. Sci. Rep. 13(1), 5314 (2023)

    ADS  Google Scholar 

  10. A. Ullah et al., Derivation of mathematical closed form expressions for certain irregular topological indices of 2D nanotubes. Sci. Rep. 13(1), 11187 (2023)

    ADS  Google Scholar 

  11. A. Hakeem, A. Ullah, S. Zaman, Computation of some important degree-based topological indices for γ- graphyne and Zigzag graphyne nanoribbon. Mol. Phys. 121, e2211403 (2023)

    ADS  Google Scholar 

  12. A. Ullah, Z. Bano, S. Zaman, Computational aspects of two important biochemical networks with respect to some novel molecular descriptors. J. Biomol. Struct. Dyn. (2023). https://doi.org/10.1080/07391102.2023.2195944

    Article  Google Scholar 

  13. V.S. Shigehalli, R. Kanabur, Computation of new degree-based topological indices of graphene. J. Math. 2016, 4341919 (2016)

    MathSciNet  MATH  Google Scholar 

  14. S. Mondal, N. De, A. Pal, Onsome new neighbourhood degree based indices. Acta Chem. Iasi 27, 31–46 (2019)

    Google Scholar 

  15. A. Ullah et al., Computational and comparative aspects of two carbon nanosheets with respect to some novel topological indices. Ain Shams Eng. J. 13(4), 101672 (2022)

    Google Scholar 

  16. S. Zaman, Cacti with maximal general sum-connectivity index. J. Appl. Math. Comput. 65(1), 147–160 (2021)

    MathSciNet  MATH  Google Scholar 

  17. A. Ullah, A. Zeb, S. Zaman, A new perspective on the modeling and topological characterization of H-Naphtalenic nanosheets with applications. J. Mol. Model. 28(8), 211 (2022)

    Google Scholar 

  18. S. Zaman et al., Structural analysis and topological characterization of sudoku nanosheet. J. Math. 2022, 5915740 (2022)

    MathSciNet  Google Scholar 

  19. A. Ullah et al., Zagreb connection topological descriptors and structural property of the triangular chain structures. Phys. Scr. 98(2), 025009 (2023)

    ADS  Google Scholar 

  20. A. Ullah et al., Network-based modeling of the molecular topology of fuchsine acid dye with respect to some irregular molecular descriptors. J. Chem. 2022, 8131276 (2022)

    Google Scholar 

  21. J.-B. Liu et al., On the laplacians and normalized laplacians for graph transformation with respect to the dicyclobutadieno derivative of [n]phenylenes. Polycycl. Aromat. Compd. 42(4), 1413–1434 (2022)

    Google Scholar 

  22. J.-B. Liu et al., The Hosoya index of graphs formed by a fractal graph. J Fractals 27(08), 1950135 (2019)

    MATH  ADS  Google Scholar 

  23. J.-B. Liu et al., Statistical analyses of a class of random pentagonal chain networks with respect to several topological properties. J. Funct. Spaces 2023, 1–17 (2023)

    MathSciNet  Google Scholar 

  24. J.-B. Liu, Y.-Q. Zheng, X.-B. Peng, The statistical analysis for Sombor indices in a random polygonal chain networks. Discret. Appl. Math. 338, 218–233 (2023)

    MathSciNet  MATH  Google Scholar 

  25. G. Chartrand, P. Erdös, O.R.J.T.C.M.J. Oellermann, How to define an irregular graph. Coll. Math. J. 19(1), 36–42 (1988)

    MathSciNet  MATH  Google Scholar 

  26. L. Von Collatz, U. Sinogowitz, Spektren endlicher grafen. in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Springer, London, 1957)

    MATH  Google Scholar 

  27. M.O.J.A.C. Albertson, The irregularity of a graph. J. Ars. Comb. 46, 219–225 (1997)

    MATH  Google Scholar 

  28. W. Luo, B.J. Zhou, On the irregularity of trees and unicyclic graphs with given matching number. J. Util. Math. 83, 141–147 (2010)

    MathSciNet  MATH  Google Scholar 

  29. P.M. Hansen, H. Mélot, Variable neighborhood search for extremal graphs 9 Bounding the irregularity of a graph. Dimacs Ser. Discrete Math. Theor. Comput. Sci. 69, 253 (2005)

    MathSciNet  MATH  Google Scholar 

  30. A.D.D. Hosam Abdo, The irregularity of graphs under graph operations. Discuss. Math. Graph Theory 34(2), 263–278 (2014)

    MathSciNet  MATH  Google Scholar 

  31. D. Dimitrov, B. Stephan, H. Abdo, The total irregularity of a graph. Discrete Math. Theor. Comput. Sci. (2014). https://doi.org/10.46298/dmtcs.1263

    Article  MathSciNet  MATH  Google Scholar 

  32. M. Tavakoli et al., Extremely irregular graphs. Kragujev J. Math. 37(1), 135–139 (2013)

    MathSciNet  MATH  Google Scholar 

  33. G.J.M.C.M.C.C. Fath-Tabar, Old and new Zagreb indices of graphs. MATCH Commun. Math. Comput. Chem. 65(1), 79–84 (2011)

    MathSciNet  MATH  Google Scholar 

  34. S. Zaman, A.N. Koam, A. Al Khabyah, A. Ahmad, The Kemeny’s Constant and spanning trees of hexagonal ring network. CMC-Comput. Mater. Contin. 73(3), 6347–6365 (2022)

    Google Scholar 

  35. S. Zaman, Spectral analysis of three invariants associated to random walks on rounded networks with 2 n-pentagons. Int. J. Comput. Math. 99(3), 465–485 (2022)

    MathSciNet  MATH  Google Scholar 

  36. Q. Li et al., Study on the normalized Laplacian of a penta-graphene with applications. Int. J. Quantum Chem. 120(9), e26154 (2020)

    Google Scholar 

  37. S. Zaman, A. Ullah, Kemeny’s constant and global mean first passage time of random walks on octagonal cell network. Math. Methods Appl. Sci. (2023). https://doi.org/10.1002/mma.9046

    Article  MathSciNet  Google Scholar 

  38. Yu, X., et al., Matrix analysis of hexagonal model and its applications in global mean-first-passage time of random walks. IEEE Access, 2023: p. 1–1.

  39. S. Zaman, X. He, Relation between the inertia indices of a complex unit gain graph and those of its underlying graph. Linear Multilinear Algebra 70(5), 843–877 (2022)

    MathSciNet  MATH  ADS  Google Scholar 

  40. R.A. Beezer, Review of: graph theory by Reinhard Diestel. (1999)

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

    ADS  Google Scholar 

  42. M.O.J.A.C. Albertson, The irregularity of a graph. Ars Comb. 46, 219–225 (1997)

    MATH  Google Scholar 

  43. D. Vukičević, A. Graovac, Valence connectivity versus Randić, Zagreb and modified Zagreb index: a linear algorithm to check discriminative properties of indices in acyclic molecular graphs. Croat. Chem. Acta 77(3), 501–508 (2004)

    Google Scholar 

  44. I.J. Gutman, Topological indices and irregularity measures. J. Bull 8, 469–475 (2018)

    MathSciNet  MATH  Google Scholar 

  45. X. Li, and I. Gutman, Mathematical Aspects of Randic-Type Molecular Structure Descriptors. Mathematical Chemistry Monographs No. 1, Kragujevac, 2006, pp. Vol. 1. 2006, Kragujevac, Serbia: Faculty of Science, University of Kragujevac (2006)

  46. T. Réti et al., Graph irregularity indices used as molecular descriptors in QSPR studies. MATCH Commun. Math. Comput. Chem 79, 509–524 (2018)

    MathSciNet  MATH  Google Scholar 

  47. H. Abdo, D. Dimitrov, W.J.C.J.O.C. Gao, On the irregularity of some molecular structures. J Can. J. Chem. 95(2), 174–183 (2017)

    Google Scholar 

  48. I. Gutman et al., Variable neighborhood search for extremal graphs 10 Comparison of irregularity indices for chemical trees. J. Chem. Inf. 45(2), 222–230 (2005)

    Google Scholar 

  49. N. Abed et al., An efficient system for intracellular delivery of beta-lactam antibiotics to overcome bacterial resistance. Sci. Rep. 5(1), 1–14 (2015)

    MathSciNet  Google Scholar 

  50. S.A.U.H. Bokhary et al., On Topological indices and QSPR analysis of drugs used for the treatment of breast cancer. Polycycl. Aromat. Compd. 42(9), 6233–6253 (2022)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, Karakoram International University Gilgit, Gilgit, 15100, Pakistan

    Asad Ullah & Anila Hamraz

  2. Department of Mathematics, University of Sialkot, Sialkot, 51310, Pakistan

    Shahid Zaman & Muniba Muzammal

Authors
  1. Asad Ullah
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  2. Shahid Zaman
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  3. Anila Hamraz
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  4. Muniba Muzammal
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The authors AU, SZ, AH and MM have equally contributed to this manuscript in all stages, from conceptualization to the write-up of final draft.

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Correspondence to Asad Ullah.

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Ullah, A., Zaman, S., Hamraz, A. et al. On the construction of some bioconjugate networks and their structural modeling via irregularity topological indices. Eur. Phys. J. E 46, 72 (2023). https://doi.org/10.1140/epje/s10189-023-00333-3

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