Article Sidebar

Submitted
October 22, 2022
Accepted
May 10, 2023
Published
March 31, 2024
Download
PDF
Statistic
Read Counter : 484 Download : 557

Downloads

Download data is not yet available.

Main Article Content

Abstract

Cellulose is one of the natural bio-polymers which have been extensively used in various
fields due to their valuable and remarkable chemical and physical properties. Due to a key ingredients
of cellulose in various product, it’s applications have widely been recognized in many industries like
pharmaceutical, bio-fuel, textiles, etc. The study of graphs using chemistry attracts a lot of researchers
globally because of its enormous application. One such application is studying topological indices is a
numerical value of a chemical graph associated to a molecular structure. This work attempts to compute
cellulose chemical structure using topological indices based on the bond like szeged, Padmakar-Ivan(PI),
weighted version of PI and szeged index and its polynomial.

Keywords

Cellulose Szeged index Padamakar-Ivan index Padmakar-Ivan polynomial Szeged polynomial

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite
KANDAN, P., & Subramanian, S. (2024). Some Bond-Additive indices and Its Polynomial of Cellulose. Journal of the Indonesian Mathematical Society, 30(1), 1–20. https://doi.org/10.22342/jims.30.1.1298.1-20
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Arockiaraj, M., Mushtaq, S., Klavˇzar, S., Celin Fiona, J., Balasubramanian, K., Szeged-like
  2. topological indices and the efficacy of the cut method: The case of melem structures, Discrete
  3. Math. Lett. 9, (2022), 49-56.
  4. Ali, P., Ajaz, P., Kirmani, K., Rugaie, O.A., and AzamKwong, F., Degree-based topological indices and polynomials of hyaluronic acid-curcumin conjugates, Saudi Pharmaceutical
  5. Journal, 28, (2020), 1093-1100.
  6. Asif, M. and Hussain, M., Topological characterization of cellulose network Comp. J. Combin.
  7. Math., 2, (2020), 21-30.
  8. Ali, A., and Dosli ˇ c´, T., Mostar index: Result and perspectives, Appl.Math.Comput.
  9. ,(2021), Article ID: 126245.
  10. Alhevaz, A., Baghipur, M. and Shang, Y., On Generalized Distance Gaussian Estrada Index
  11. of Graphs Symmetry, 11(10), 1276, 2019.
  12. Arokiaraj, M., Clement, J., Tratnik, N., Mushtaq, S., and Balasubramanian, K.,Weighted
  13. Mostar indices as Mostar indices as measures of molecular peripheral shapes with application
  14. to graphene, graphdiyne and graphdiyne nanoribbons, SAR QSAR Environ.Res., 31, (2020),
  15. -208.
  16. Ashrafi, A.R., Ghorbani, M., and Jalali, M., The PI and Edge Szeged Polynomials of an
  17. Infinite Family of Fullerenes, Nanotubes and Carbon Nanostructures, 18(2), (2010), 1536-
  18. Ahmad, M., Saeed, M., Javaid, M., and Bonyah, E., Molecular Descriptor Analysis of Certain
  19. Isomeric Natural Polymers, Hindawi Journal of Chemistry, 26, (2021), Article ID 9283246.
  20. Brezovnik, S. and Tratnik, N., General cut method for computing szeged-like topological
  21. indices with application to molecular graphs, International Journal of Quantum Chemistry,
  22. (2), (2021), Article ID: e26530.
  23. Cash, G.G., Relationship Between the Hosoya Polynomial and the Hyper-Wiener Index,
  24. Applied Mathematics Letters, 15, (2002), 893-895.
  25. Cruz-Medina, R., Ayala-Hern´andez, D.A. et al, Curing of Cellulose Hydro gels by UV Radiation for Mechanical Reinforcement, MDIP, 13, (2021), 23-42.
  26. Dobrynin, A., The Szeged and Wiener indices of line graphs,MATCH Commun. Math. Comput. Chem., 79, (2018), 743-756.
  27. Dosli ˇ c´, T. and Martinjak, I., Sˇkrekovski, R., Spuzevi ˇ c´, S.T. and Zubac, I., Mostar index,
  28. Journal of mathematical chemistry, 56(10), (2018), 2995-3013.
  29. Ghorbani, M. and Jalali, M., The Vertex PI, Szeged and Omega Polynomials of Carbon
  30. Nanocones CNC4[n], MATCH Commun. Math. Comput. Chem. 62, (2009), 353-362.
  31. Ghorbani, M. and Hemmasi, M., The Vertex PI and Szeged Polynomials of an Infinite Family
  32. of Fullerenes, Journal of Computational and Theoretical Nanoscience, 7, (2010), 2411-2415.
  33. Gutman, I. and Dobrynin, A., The Szeged index - a success story,Graph Theory Notes New
  34. York, 34, (1998), 37-44.
  35. Gutman, I. and Ashrafi, A.R., On the PI Index of Phenylenes and their Hexagonal Squeezes,
  36. MATCH Commun. Math. Comput. Chem., 60, (2008), 135-142.
  37. Gupta, P.K., Raghunath, S.S., Prasanna, D.V., Venkat, P., Shree, D.V., Chithananthan,
  38. C., Choudhary, S., Surender, K., and Geetha, K., An Update on Overview of Cellulose, Its
  39. Structure and Applications, web of science, intech open, (2019), 1-23
  40. Ilic´, A. and M ilosavljevic´, N., The weighted vertex PI index, Mathematical and Modeling,
  41. ,(2013), 627-631.
  42. Kirmani, S.A.K., Ali, P. and Azam, F., Topological indices and QSPR/QSAR analysis of
  43. some antiviral-drugs being investigated for the treatment of COVID-19 patients, Int J Quantum Chem., 121, (2021), Article ID: e26594.
  44. Khalaf, A.J.M., et al, Degree-based topological indices and polynomial of cellulose, Journal
  45. of prime in mathematics, 17(1), (2021), 70-78.
  46. Kandan, P. and Subramanian, S., On Mostar index of graph, Advances in Mathematics:
  47. Scientific Journal, 10(4), (2021), 2115-2129.
  48. Kandan, P., Subramanian, S., and Rajesh, P., Weighted Mostar indices of certain graphs,
  49. Advance in mathematics:Scientific journal, 10(9), (2021), 3093-3111.
  50. Kandan, P. and Subramanian, S., Computation of Weighted PI and Szeged Indices of Conical
  51. Graph, Indian Journal of Natural Sciences, 12(69), 2021, 36933-36941.
  52. Kandan, P. and Subramanian, S., Mostar index of Conical and Generalized gear graph Commun. Combin., Cryptogr. and Computer Sci., 2, (2022), 1-9.
  53. Kandan, P. and Subramanian, S., Some bound-additive indices of graohs (ICDM2021-MSU)
  54. -93-91077-53-2, 1-7, (confrence procceding).
  55. Kandan, P. and Subramanian, S., Weighted PI and Szeged indices of generlized gear graph,
  56. Indian Journal of Natural Sciences, 13(72), (2022), 41816-41823.
  57. Kandan, P., Subramanian, S., and Rajesh, P., Calculating PI related indices and their polynomial of Hyaluronic Acid and Conjugates, J. Indones. Math. Soc., 28(2), (2022), 194-214.
  58. Kumar, R., Sharma, R.K., and Singh, A.P., Grafted cellulose: A bio-based polymer for durable
  59. applications, Polym. Bull., 75, (2018), 2213-2242.
  60. Khadikar, P.V., Karmarkar, S., Agrawal, V.K., Singh, J., Shrivastava, J., Lukovits, I., and
  61. Diudea, M.V., Szeged index Applications for drug modeling, Lett. Drug Design Disc., 2,
  62. (2005), 606-624.
  63. Khadikar, P.V. and Karmarkar, S., A novel PI index and its applications to QSPR/QSAR
  64. studies, J. Chem. Inf. Comput. Sci., 41, (2001), 934-949.
  65. Khalifeh, M.H., Yousefi, H., and Ashrafi, A.R., Vertex and edge PI-indices of Cartesian
  66. Product graphs, Discrete Appl. Math., 156, (2008), 1780-1789.
  67. Mirzargar, M., PI, Szeged and Edge Szeged Polynomials of a Dendrimer Nanostar, MATCH
  68. Commun. Math. Comput. Chem., 62, (2009), 363-370.
  69. Makowsky, J.A., Ravve, E.V., and Blanchard, N.K., On the location of roots of graph polynomials, European Journal of Combinatorics, 41, (2014), 1-19.
  70. Pattabiraman, K. and Kandan, P., Weighted szeged index of graphs, Bulletin of the International mathematical virtual institute, 8, (2018), 11-19.
  71. Pattabiraman, K. and Kandan, P., On weighted PI index of graphs, Electronic notes in
  72. discrete mathematics, 53, (2016), 225-238.
  73. Shang, Y., A remark on the chromatic polynomial of in comparability graphs of posets, PLoS
  74. ONE, 10(3), (2014), 17-31.
  75. Shang, Y., Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs
  76. Mathematics, 2020, 8, 1063.
  77. Shang, Y., Sombor index and degree-related properties of simplicial networksApplied Mathematics and Computation, 419. p. 126881. ISSN 0096-3003.
  78. Tranik, N., Computing weighted Szeged and PI indices from quotient graphs, Int J Quantum
  79. Chem., (2019), Article ID: e26006.
  80. Trinajstic, N., Chemical Graph Theory, CRC Press, Boca Raton, FL, USA, Volum I/II, 1983.
  81. Tang, Z., Wu, Z., Cheu, H., and Deng, H., This distance spectrum ot two new operations of
  82. graphs,Transactions on Combinatorics, 9(3), (2020), 125-138.
  83. Wang, J., Wang, Y., Wang, Y., and Zheng, L., Computational on the topological indices of
  84. hyaluronic acid,Journal of Applied Analysis and Computation, 3(10), (2020), 1193-1198.
  85. Wang, Z., Mao, Y., Das, K.C., and Shang, Y., Nordhaus–Gaddum-Type Results for the
  86. Steiner Gutman Index of Graphs Symmetry, 12, 2020, 1711