Further Results for Some Eccentric Based Indices


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Аннотация

Background:Topological indices have a significant role in determining a molecule’s topology in the light of theoretical chemistry.

Objectives:This study aimed to find new bounds for some eccentric-based topological indices.

Methods:We used comparison theorem for integrals.

Results:We found new bounds for the eccentric-based harmonic index and atom-bond connectivity index. Our results are better than previous results in the literature.

Conclusion:This study has contributed to the chemical graph theory literature by giving a new method to find eccentric-based topological indices with lower and upper bounds.

Об авторах

Havva Kirgiz

Department of Mathematics, Selçuk University

Автор, ответственный за переписку.
Email: info@benthamscience.net

Ayşe Maden

Department of Mathematics, Selçuk University

Email: info@benthamscience.net

Список литературы

  1. Wiener, H. Structural determination of paraffin boiling points. J. Am. Chem. Soc., 1947, 69(1), 17-20. doi: 10.1021/ja01193a005 PMID: 20291038
  2. Ali, A.; Raza, Z.; Bhatti, A.A. A note on the minimum reduced reciprocal randic index of n-vertex unicyclic graphs. Kuwait J. Sci., 2016, 44, 27-33.
  3. Buyukkose, S.; Cangul, I.N. Some notes on Randi´c index. Boletim da Sociedade Paranaense de Matemática, 2022, 40, 1-7. doi: 10.5269/bspm.47213
  4. Liu, C.; Yan, Z.; Li, J. Extremal trees for the general Randic index with a given domination number. Bull. Malays. Math. Sci. Soc., 2022, 45(2), 767-792. doi: 10.1007/s40840-021-01235-3
  5. Alfuraidan, M.R.; Das, K.C.; Vetrík, T.; Balachandran, S. General Randić index of unicyclic graphs with given diameter. Discrete Appl. Math., 2022, 306, 7-16. doi: 10.1016/j.dam.2021.09.016
  6. Ali, A.; Raza, Z.; Bhatti, A. On the augmented zagreb index. Kuwait J. Sci., 2016, 43, 48-63.
  7. Ali, A.; Bhatti, A.A. A note on the augmented Zagreb index of cacti with fixed number of vertices and cycles. Kuwait J. Sci., 2016, 43, 11-17.
  8. Liu, J-B.; Wang, C.; Wang, S.; Wei, B. Zagreb indices and multiplicative zagreb indices of eulerian graphs. Bull. Malays. Math. Sci. Soc., 2019, 42(1), 67-78. doi: 10.1007/s40840-017-0463-2
  9. Martínez-Pérez, A.; Rodríguez, J.M. New lower bounds for the first variable Zagreb index. Discrete Appl. Math., 2022, 306, 166-173. doi: 10.1016/j.dam.2021.09.030
  10. Zhang, P. The zagreb index of several random models. J Stochastic Anal., 2022, 3, 1.
  11. Divya, A.; Manimaran, A. Extremal trees for the geometricarithmetic index with the maximum degree. Disc. Math. Lett., 2022, 9, 38-43.
  12. Vujošević, S.; Popivoda, G.; Kovijanić Vukićević, Ž.; Furtula, B.; Škrekovski, R. Arithmetic–geometric index and its relations with geometric–arithmetic index. Appl. Math. Comput., 2021, 391, 125706. doi: 10.1016/j.amc.2020.125706
  13. Liang, M.; Cheng, B.; Liu, J. Solution to the minimum harmonic index of graphs with given minimum degree. Transact. Combinat., 2018, 7, 25-33.
  14. Martınez-Martınez, C.; Mendez-Bermudez, J.; Rodrıguez, J.M. Sigarreta, Computational and analytical studies of the harmonic index in erdös–renyi models. J. M. MATCH Commun. Math. Comput. Chem., 2021, 85, 395.
  15. Chen, C.; Liu, M.; Chen, X.; Lin, W. On general A B C -type index of connected graphs. Discrete Appl. Math., 2022, 315, 27-35. doi: 10.1016/j.dam.2022.03.013
  16. Ali, A.; Das, K.C.; Dimitrov, D.; Furtula, B. Atom–bond connectivity index of graphs: A review over extremal results and bounds. Disc. Math. Lett., 2021, 5(1), 68-93. doi: 10.47443/dml.2020.0069
  17. Randic, M. Characterization of molecular branching. J. Am. Chem. Soc., 1975, 97(23), 6609-6615. doi: 10.1021/ja00856a001
  18. Ghorbani, M.; Hosseinzadeh, M. A new version of Zagreb indices. Filomat, 2012, 26(1), 93-100. doi: 10.2298/FIL1201093G
  19. Farahani, M.R. Eccentricity version of atom-bond connectivity index of benzenoid family abc5 (hk). World Appl. Sci. J., 2013, 21, 1260-1265.
  20. Ediz, S.; Farahani, M.R.; Imran, M. On novel harmonic indices of certain nanotubes. Int. J. Adv. Biotechnol. Res., 2017, 8, 87-92.
  21. Du, Z.; Jahanbai, A.; Sheikholeslami, S.M. Relationships between randic index and other topological indices. Comm. Combinat. Opti., 2021, 6, 137-154.
  22. Liu, J.B.; Zhao, J.; He, H.; Shao, Z. Valency-based topological descriptors and structural property of the generalized sierpinski networks. J. Stat. Phys., 2019, 177(6), 1131-1147. doi: 10.1007/s10955-019-02412-2
  23. Fajtlowicz, S. On conjectures of graffiti-ii. Congr. Numer, 1987, 60, 187-197.
  24. Estrada, E.; Torres, L.; Rodriguez, L.; Gutman, I. An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes. Indian J. Chem., 1998, 37, 849-855.
  25. Kırgız, H.; Maden, A.D. New bounds for some topological indices. Int. J. Found. Comput. Sci., 2022, 33(06n07), 953-965. doi: 10.1142/S0129054122420230
  26. Sowaity, M.I.; Pavithra, M.; Sharada, B.; Naji, A.M. Eccentric harmonic index of a graph. Arab J. Basic Appl. Sci., 2019, 26(1), 497-501. doi: 10.1080/25765299.2019.1688914
  27. Xing, R.; Zhou, B.; Du, Z. Further results on atom-bond connectivity index of trees. Discrete Appl. Math., 2010, 158(14), 1536-1545. doi: 10.1016/j.dam.2010.05.015
  28. Lee, D.W. Some lower and upper bounds on the third ABC index. AKCE Int. J. Graphs Combinat., 2016, 13(1), 11-15. doi: 10.1016/j.akcej.2016.02.002

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