Chemical Relevance and Expected Values of K-Banhatti Indices for Random Cyclodecane Chains
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Keywords:
Chemical Graph Theory; Topological Indices; Cyclodecane Chains; Genes; Pharmacogenomics; Expected Values; ComparisonsAbstract
Cyclodecane, a remarkable cyclic hydrocarbon, comprises larger molecular structures or polymers formed by interlinking multiple cyclodecane rings. These interactions are crucial in pharmacogenomics, as the strategic design of a compound decisively influences its interactions with gene products, including enzymes and receptors. In the dynamic field of mathematical chemistry, chemical graph theory plays a crucial role in enhancing our understanding of the complex properties of chemical compounds. Currently, one of the most promising areas of research involves the calculation of topological indices. Among these indices, the First K hyper-Banhatti index, Second K hyper-Banhatti index, Modified first K-Banhatti index, and Modified second K-Banhatti index serve as important topological descriptors that significantly contribute to our analysis of the physicochemical, biological, and structural characteristics of chemical compounds. This article aims to determine the expected values of these topological descriptors for random cyclodecane chains, presenting our findings in significant numerical tables and insightful graphical representations. Through this exploration, we aim to deepen our appreciation of how these descriptors impact the fundamental properties of chemical compounds, paving the way for future discoveries in this compelling field.
References
H. Wiener, “Structure determination of paraffin boiling points,” Journal of the American Chemical Society, vol. 69, no. 1, pp. 17-20, 1947, doi: https://doi.org/10.1021/ja01193a005.
H. Y. Deng, “Wiener indices of spiro and polyphenyl hexagonal chains,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 634-644, 2012, https://doi.org/10.1016/j.mcm.2011.08.037.
M. Randiacute{c}, “Characterization of molecular branching,” Journal of the American Chemical Society, vol. 97, pp. 6609-6615, 1975, doi: https://doi.org/10.1021/ja00856a001.
I. Gutman, J. W. Kennedy, and L. V. Quintas, “Wiener numbers of random benzenoid chains,” Chemical Physics Letters, vol. 173, no. 4, pp. 403-408, 1990, https://doi.org/10.1016/0009-2614(90)85292-K.
I. Gutman, and K. Das, “The first Zagreb index 30 years after,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 50, pp. 83-92, 2004.
View more references (26)
J. L. Zhang, X. H. Peng, and H. L. Chen, “The Limiting Behaviours for the Gutman Index, Schultz Index, Multiplicative Degree-Kirchhoff Index and Additive Degree-Kirchhoff Index of a Random Polyphenylene Chain,” Discrete Applied Mathematics, vol. 299, pp. 62-73, 2021, doi: https://doi.org/10.1016/j.dam.2021.04.016.
L. L. Zhang, Q. S. Li, S. C. Li, and M. J. Zhang, “The expected values for the Schultz Index, Gutman Index, multiplicative degree-Kirchhoff Index and additive degree-Kirchhoff index of a random polyphenylene chain,” Discrete Applied Mathematics, vol. 282, pp. 243-256, 2020, doi: https://doi.org/10.1016/j.dam.2019.11.007.
D. Bonchev, “Information Theoretic Indices for Characterization of Molecular Structure,” Research Studies Press-Wiley, Chichester, 1983.
D. Vukicheck{c}eviacute{c}, and M. Gacheck{s}perov, “Bond Additive Modeling 1. Adriatic Indices,” Croatica Chemica Acta, vol. 83, no. 3, pp. 243-260, 2010.
H. C. Liu, R. W. Wu, and L. H. You, “Three Types of Kirchhoff Indices in the Random Cyclooctane Chains,” Journal of South China Normal University (Natural Science Edition), vol. 53, no. 2, pp. 96-103, 2021.
S. L. Wei, X. L. Ke, and G. L. Hao, “Comparing the expected values of atom-bond connectivity and geometric-arithmetic indices in random spiro chains,” Journal of Inequalities and Applications, vol. 2018, pp. 45, 2018, https://doi.org/10.1186/s13660-018-1628-8.
A. Ali, A. A. Bhatti, and Z. Raza, “Topological study of tree-like polyphenylene systems, spiro hexagonal systems and polyphenylene dendrimer nanostars,” Quantum Matter, vol. 5, no. 4, pp. 534-538, 2016, https://doi.org/10.1166/qm.2016.1345
A. Ali, Z. Raza, and A. A. Bhatti, “Extremal pentagonal chains with respect to degree-based topological indices,” Canadian Journal of Chemistry, vol. 94, pp. 870-876, 2016, https://doi.org/10.1139/cjc-2016-0308.
A. Ali, Z. Raza, and A. A. Bhatti, “Some vertex-degree based topological indices of cacti,” Ars Combinatoria, vol. 144, pp. 195-206, 2019.
A. Jahanbani, “The expected values of the first Zagreb and Randiacute{c} indices in random polyphenyl chains,” Polycyclic Aromatic Compounds, vol. 42, no. 4, pp. 1851-1860, 2022, https://doi.org/10.1080/10406638.2020.1809472.
G. Huang, M. Kuang, and H. Deng, “The expected values of Hosoya index and Merrifield-Simmons index in a random polyphenylene chain,” Journal of Combinatorial Optimization, vol. 32, pp. 550-562, 2016, https://doi.org/10.1007/s10878-015-9882-x
G. Huang, M. Kuang, and H. Deng, “The expected values of Kirchhoff indices in the random polyphenyl and spiro chains,” Ars Mathematica Contemporanea, vol. 9, no. 2, pp. 207-217, 2015, https://doi.org/10.26493/1855-3974.458.7b0
P. check{Z}igert Pletercheck{s}ek, “The edge-Wiener index and the edge-hyper-Wiener index of phenylenes,” Discrete Applied Mathematics, vol. 255, pp. 326-333, 2019, https://doi.org/10.1016/j.dam.2018.07.024.
R. Mojarad, B. Daneshian, and J. Asadpour, “Omega and related polynomials of phenylenes and their hexagonal squeezes,” Optoelectronics and Advanced Materials-Rapid Communications, vol. 10, no. 1, pp. 113-116, 2016.
V. R. Kulli, “Computing Banhatti indices of networks,” International Journal of Advances in Mathematics, vol. 2018, no. 1, pp. 31-40, 2018.
V. R. Kulli, “On K Banhatti Indices of Graphs,” Journal of Computer and Mathematical Sciences, vol. 7, no. 4, pp. 213-218, 2016.
V. R. Kulli, “On K hyper-Banhatti Indices and coindices of graphs,” International Research Journal of Pure Algebra, vol. 6, no. 5, pp. 300-304, 2016.
V. R. Kulli, “On K Banhatti indices and K hyper-Banhatti indices of V-Phenylenic nanotubes and nanotorus,” Journal of Computer and Mathematical Sciences, vol. 7, no. 6, pp. 302-307, 2016.
V. R. Kulli, B. Chaluvaraju, and H. S. Baregowda, “K-Banhatti and K hyper-Banhatti indices of windmill graphs,” South East Asian Journal of Mathematics and Mathematical Sciences, vol. 13, no. 1, pp. 11-18, 2017.
F. Dayan, M. Javaid, M. Zulqarnain, M. T. Ali, and B. Ahmad, “Computing Banhatti indices of hexagonal, honeycomb and derived graphs,” American Journal of Mathematical and Computer Modelling, vol. 3, no. 2, pp. 38-45, 2018, https://doi.org/10.11648/j.ajmcm.20180302.11.
B. Chunsong, A. Naeem, S. Yousaf, A. Aslam, F. Tchier, and A. Issa, “Exploring expected values of topological indices of random cyclodecane chains for chemical insights,” Scientific Reports, vol. 14, pp. 10065, 2024, https://doi.org/10.1038/s41598-024-60484-x.
W. Wei, and L. Shuchao, “Extremal phenylene chains with respect to the coefficients sum of the permanental polynomial, the spectral radius, the Hosoya index and the Merrifield-Simmons index,” Discrete Applied Mathematics, vol. 271, no. 1, pp. 205-217, 2019, https://doi.org/10.1016/j.dam.2019.07.024.
W. Yang, and F. Zhang, “Wiener index in random polyphenyl chains,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 68, no. 1, pp. 371-376, 2012.
X. L. Chen, B. Zhao, and P. Y. Zhao, “Six-membered ring spiro chains with extremal Merrified-Simmons index and Hosoya index,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 62, pp. 657-665, 2009.
X. Y. Li, G. P. Wang, H. Bian, and R. W. Hu, “The Hosoya polynomial decomposition for polyphenyl chains,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 67, pp. 357-368, 2012.
Z. Raza, “The Harmonic and Second Zagreb Indices in Random Polyphenyl and Spiro Chains,” Polycyclic Aromatic Compounds, vol. 42, no. 3, pp. 671-680, 2022, https://doi.org/10.1080/10406638.2020.1749089.