Calculation of topological indices based on M-polynomial for polytrimethylene terephthalate

Document Type : Full Length Article

Authors

1 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.

2 Department of Mathematics, Statistics and Computer Science

Abstract

Polytrimethylene terephthalate is an extensively utilized thermoplastic industrial polymer characterized by a low melting point and minimal water absorption and it follows the general molecular formula $(C_{11}H_{10}O_{4}){n}$. It is interesting to chemists and engineering researchers due to its application in various industries, especially in textiles and engineering thermoplastics. In this article, the general formulas of some degree-based topological indices are obtained via M-polynomials for Polytrimethylene terephthalate. Calculating indices via these formulas does not require counting the degree of vertices or edge partitioning and can only be calculated by having the number of Polytrimethylene terephthalate monomers. The obtained results are displayed numerically and graphically, then the topological indices are graphically compared.

Graphical Abstract

Calculation of topological indices based on M-polynomial for polytrimethylene terephthalate

Keywords

Main Subjects


[1] Rath, Abjesh Prasad, P. Santhana Gopala Krishnan, Krishnan Kanny, Studies on (polytrimethylene
terephthalate)/graphene oxide/f-MWCNT hybrid nanocomposites, Discover Nano 19 (2024) 1–
12.
[2] Eren, Semiha, I. Ozcan, I. Yigit, H. Aksel Eren, Waterless dyeing of polytrimethylene terephthalate
and polybutylene terephthalate fabrics via supercritical carbon dioxide, The Journal of Supercritical Fluids 201 (2023) 106026.
[3] J. Devroede, Study of the THF formation during the TPA-based synthesis of PBT, [Phd Thesis 1
(Research TU/e/Graduation TU/e), Chemical Engineering and Chemistry], Technische Universiteit Eindhoven. (2007), doi:10.6100/IR630627.
[4] E. Deutsch, S. Klavzar, M-polynomial and degree-based topological indices, arXiv preprint arXiv:
1407.1592 (2014).
[5] M. Ghorbani, S. Rahmani, M. Eslampoor, Some new results on Mostar index of graphs, Iranian J.
Math. Chem. 11 (2020) 33–42.
[6] I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput.
Chem. 50 (2004) 83–92.
[7] I. Gutman, N. Trinajsti´c, Graph theory and molecular orbitals. Total π-electron energy of alternant
hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.
[8] I. Gutman, N. Trinajsti´c, C. F. Wilcox, Graph theory and molecular orbitals XII Acyclic polyenes, J.
Chem. Phys. 62 (1975) 3399–3405.
[9] K. C. Das, I. Gutman, B. Furtula, On atom-bond connectivity index, Filomat 26 (2012) 733–738.
[10] E. Estrada, L. Torres, L. Rodriguez, I. Gutman, An atom-bond connectivity index: modelling the
enthalpy of formation of alkanes, Indian J. Chem. 37A (1998) 849–855.
[11] C. K. Gupta, V. Lokesha, S. B. Shwetha, P. S. Ranjini, On the symmetric division deg index of graph,
Southeast Asian Bulletin of Mathematics 40 (2016) 41–51.
[12] L. Zhong, The harmonic index for graphs, Appl. Math. Lett. 25 (2012) 561–566.
[13] B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015) 1184–1190.
[14] I. Gutman, M. Togan, A. Yurttas, A. S. Cevik, I. N. Cangul, Inverse problem for sigma index,
MATCH Commun. Math. Comput. Chem. 79 (2018) 491–508.
[15] S. Fajtlowicz, On conjectures of Graffiti, Discrete Math. 72 (1988) 113–118.
[16] G. H. Shirdel, H. Rezapour, A. M. Sayadi, The Hyper-Zagreb index of graph operations, Iranian J.
Math. Chem. 4 (2013) 213–220.
[17] V. R. Kulli, The gourava indices and coindices of graphs, Ann. Pure Appl. Math. 14 (2017) 33–38.
[18] H. Rezapour, R. Nasiri, S. Mousav, The hyper-Zagreb index of trees and unicyclic graphs, Iranian
J. Math. Sci. Inf. 18 (2023) 41–54.
[19] Z. Rajabinejad, S. Mohammadian-Semnani, Calculation of topological indices based on the
distance of polyacenes without edge counting, Polycyclic Aromatic Compounds (2023) 1–12,
doi:10.1080/10406638.2023.2276244.
[20] U. Sheikh. S. Rashid, C. Ozel, R. Pincak, On Hosoya polynomial and subsequent indices of C4C8(R)
and C4C8(S) nanosheets, Symmetry 14 (2022) 1349, doi:10.3390/sym14071349.
[21] E. Deutsch, S. Klavžar, M-polynomial and degree-based topological indices, Iranian J. Math.
Chem. 6 (2015) 93–102.
[22] M. Ajmal, W. Nazeer, M. Munir, S. M. Kang, C. Y. Jung, The M-Polynomials and topological indices
of generalized prism network, Int. J. Math. Anal. 11 (2017) 293–303.
Volume 9, Issue 3
September 2024
Pages 181-190
  • Receive Date: 01 August 2024
  • Revise Date: 11 August 2024
  • Accept Date: 25 August 2024
  • Publish Date: 01 September 2024