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Degree–based topological indices of a general random chain | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 دی 1403 اصل مقاله (615.67 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2024.30080.2301 | ||
نویسندگان | ||
Saylé Sigarreta* 1؛ Hugo Cruz Suárez1؛ Sergio Torralbas Fitz2 | ||
1Facultad de Ciencias F´ısico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, México | ||
2Department of Orthopedic Oncology, University of Miami - Miller School of Medicine, Miami, Florida, United States | ||
چکیده | ||
In this paper, we examine a specific type of random chains and propose a unified approach to studying the degree-based topological indices, including their extreme values. We derive explicit analytical expressions for the expected values and variances of these indices and we establish the asymptotic behavior of the indices. Specifically, we analyze the first Zagreb index, Sombor index, harmonic index, Geometric-Arithmetic index, Inverse Sum Index, and the second Zagreb index for various general random chains, including random phenylene, random polyphenyl, random hexagonal, and linear chains. | ||
کلیدواژهها | ||
Random chains؛ Topological indices؛ Extreme values؛ Markov processes | ||
مراجع | ||
[1] A. Ali, Z. Raza, and A.A. Bhatti, Bond incident degree (BID) indices of polyomino chains: A unified approach, Appl. Math. Comput. 287 (2016), 28–37. https://doi.org/10.1016/j.amc.2016.04.012
[2] S. Alikhani and N. Ghanbari, Sombor index of polymers, MATCH Commun. Math. Comput. Chem. 86 (2021), 715–728.
[3] S. Amin, A.U. Rehman Virk, M.A. Rehman, and N. Ali Shah, Analysis of dendrimer generation by Sombor indices, J. Chem. 2021 (2021), no. 1, 9930645. https://doi.org/10.1155/2021/9930645
[4] H. Chen, W. Li, and J. Wang, Extremal values on the sombor index of trees, MATCH Commun. Math. Comput. Chem. 87 (2022), no. 1, 23–49.
[5] K.C. Das, A.S. Çevik, I.N. Cangul, and Y. Shang, On sombor index, Symmetry 13 (2021), no. 1, 140. https://doi.org/10.3390/sym13010140
[6] A. A. Dobrynin, I. Gutman, S. Klavžar, and P. Žigert, Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002), no. 3, 247–294. https://doi.org/10.1023/A:1016290123303
[7] T. Došlić, T. Réti, and D. Vukičević, On the vertex degree indices of connected graphs, Chem. Phys. Lett. 512 (2011), no. 4-6, 283–286. https://doi.org/10.1016/j.cplett.2011.07.040
[8] X. Fang, L. You, and H. Liu, The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs, Int. J. Quantum Chem. 121 (2021), no. 17, e26740. https://doi.org/10.1002/qua.26740
[9] A. Farooq, M. Habib, A. Mahboob, W. Nazeer, and S.M. Kang, Zagreb polynomials and redefined Zagreb indices of dendrimers and polyomino chains, Open Chem. 17 (2019), no. 1, 1374–1381. https://doi.org/10.1515/chem-2019-0144
[10] A. Granados, A. Portilla, Y. Quintana, and E. Tour´ıs, New bounds for variable topological indices and applications, J. Math. Chem. 62 (2024), no. 6, 1435–1453. https://doi.org/10.1007/s10910-024-01593-w
[11] A. Gut, Probability: a Graduate Course, Springer, 2006.
[12] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), 11–16.
[13] J.C. Hernández, J.M. Rodríguez, O. Rosario, and J.M. Sigarreta, Extremal problems on the general Sombor index of a graph, AIMS Math. 7 (2022), no. 5, 8330–8343. https://doi.org/10.3934/math.2022464
[14] N. Iqbal, A.A. Bhatti, A. Ali, and A.M. Alanazi, On bond incident connection indices of polyomino and benzenoid chains, Polycycl. Aromat. Compd. 43 (2022), no. 2, 1000–1007. https://doi.org/10.1080/10406638.2022.2035414
[15] A. Jahanbani, The first Zagreb and Randić indices in random spiro chains, Polycycl. Aromat. Compd. 42 (2020), no. 4, 1842–1850. https://doi.org/10.1080/10406638.2020.1809471
[16] X. Ke, S. Wei, and J. Huang, The atom-bond connectivity and geometric-arithmetic indices in random polyphenyl chains, Polycycl. Aromat. Compd. 41 (2021), no. 9, 1873–1882. https://doi.org/10.1080/10406638.2019.1703763
[17] V.R. Kulli, Graph indices, Handbook of Research on Advanced Applications of Graph Theory in Modern Society (M. Pal, S. Samanta, and A. Pal, eds.), IGI Global, Oxford, UK, 2020, pp. 66–91.
[18] Y.C. Kwun, A. Farooq, W. Nazeer, Z. Zahid, S. Noreen, and S.M. Kang, Computations of the $M$-polynomials and degree-based topological indices for dendrimers and polyomino chains, Int. J. Anal. Chem. 2018 (2018), 1709073. https://doi.org/10.1155/2018/1709073
[19] H. Liu, H. Chen, Q. Xiao, X. Fang, and Z. Tang, More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons, Int. J. Quantum Chem. 121 (2021), no. 17, e26689. https://doi.org/10.1002/qua.26689
[20] H. Liu, L. You, Z. Tang, and J.B. Liu, On the reduced Sombor index and its applications, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 3, 729–753.
[21] D. Mühlbacher, M. Scharber, M. Morana, C. Brabec, Z. Zhu, D. Waller, and R. Gaudiana, High photovoltaic performance of a low-bandgap polymer, Adv. Mater. 18 (2006), no. 21, 2884–2889. https://doi.org/10.1002/adma.200600160
[22] K. Müllen, J.R. Reynolds, and T. Masuda, Conjugated Polymers: a Practical Guide to Synthesis, Royal Society of Chemistry, 2013.
[23] A. Pegu, B. Deka, I.J. Gogoi, and A. Bharali, Two generalized topological indices of some graph structures, J. Math. Comput. Sci. 11 (2021), no. 5, 5549–5564. https://doi.org/10.28919/jmcs/6040
[24] J. Rada, J.M. Rodríguez, and J.M. Sigarreta, On integral Sombor indices, Appl. Math. Comput. 452 (2023), 128036. https://doi.org/10.1016/j.amc.2023.128036
[25] A. Rauf, M. Naeem, and S.U. Bukhari, Quantitative structure–property relationship of ev-degree and ve-degree based topological indices: physico-chemical properties of benzene derivatives, Int. J. Quantum Chem. 122 (2022), no. 5, e26851. https://doi.org/10.1002/qua.26851
[26] Z. Raza, The expected values of arithmetic bond connectivity and geometric indices in random phenylene chains, Heliyon 6 (2020), no. 7, e04479. https://doi.org/10.1016/j.heliyon.2020.e04479
[27] Z. Raza, The expected values of some indices in random phenylene chains, Eur. Phys. J. Plus 136 (2021), no. 1, 1–15. https://doi.org/10.1140/epjp/s13360-021-01082-y [28] Z. Raza and M. Imran, Expected values of some molecular descriptors in random cyclooctane chains, Symmetry 13, no. 11, 2197. https://doi.org/10.3390/sym13112197
[29] Z. Raza, K. Naz, and S. Ahmad, Expected values of molecular descriptors in random polyphenyl chains, Emerg. Sci. J. 6 (2022), no. 1, 151–165. https://doi.org/10.28991/ESJ-2022-06-01-012
[30] T.A. Severini, Elements of Distribution Theory, Cambridge University Press, 2005.
[31] Y. Shang, Distance Estrada index of random graphs, Linear Multilinear Algebra 63 (2015), no. 3, 466–471. https://doi.org/10.1080/03081087.2013.872640
[32] Z. Shao, A. Jahanbani, and S.M. Sheikholeslami, Multiplicative topological indices of molecular structure in anticancer drugs, Polycycl. Aromat. Compd. 42 (2022), no. 2, 475–488. https://doi.org/10.1080/10406638.2020.1743329
[33] S. Sigarreta and H. Cruz-Suárez, Zagreb connection indices on polyomino chains and random polyomino chains, Open Math. 22 (2024), no. 1, 20240057. https://doi.org/10.1515/math-2024-0057
[34] S.C. Sigarreta, S.M. Sigarreta, and H. Cruz-Suárez, On degree–based topological indices of random polyomino chains, Math. Biosci. Eng. 19 (2022), no. 9, 8760–8773. https://doi.org/10.3934/mbe.2022406
[35] S.C. Sigarreta, S.M. Sigarreta, and H. Cruz-Suárez, On bond incident degree indices of random spiro chains, Polycycl. Aromat. Compd. 43 (2023), no. 7, 6306–6318. https://doi.org/10.1080/10406638.2022.2118795
[36] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005
[37] S. Yousaf, Z. Iqbal, S. Tariq, A. Aslam, F. Tchier, and A. Issa, Computation of expected values of some connectivity based topological descriptors of random cyclooctane chains, Sci. Rep. 14 (2024), Article number: 7713. https://doi.org/10.1038/s41598-024-57175-y
[38] W. Zhang, L. You, H. Liu, and Y. Huang, The expected values and variances for Sombor indices in a general random chain, Appl. Math. Comput. 411 (2021), 126521. https://doi.org/10.1016/j.amc.2021.126521 | ||
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