Abstract
This research delves into a comprehensive investigation of a specific group of alkanes, with the primary objective of establishing meaningful associations between their inherent physical attributes and a set of graphical parameters ranging from topological indices to their associated graphical entropies. Though there are countless techniques to relate molecular structure and physical properties of chemical compounds, the pursuit has often been pricey and arduous. With a view to curb the expense and intense labour, this work focuses on attaining some of these properties using graphical interpretations and statistical interventions. Driven by this objective, we compute Sombor index, a recently developed topological tool and some of its variants for all structural isomers of alkanes with carbon range four to nine. Furthermore, our study employs multiple regression analysis to explore their connections with some physical attributes of alkanes while concurrently addressing the challenge posed by multicollinearity. We have adopted the technique of robust regression to scale down the impact of outliers in the dataset, while generating regression models. Further, the established results are justified with a 10-fold cross validation process and a comparison with the results obtained from different topological indices. The results of this research contribute a valuable insight to the fields of chemical informatics and structural analysis, offering an enhanced comprehension of the interplay between molecular structure and physical attributes within alkanes.
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References
I. Gutman, Geometric approach to degree-based topological indices: Sombor indices. MATCH Commun. Math. Comput. Chem 86(1), 11–16 (2021)
V. Kulli, Neighborhood Sombor indices. Int. J. Math. Trends Technol. 68(6), 195–202 (2022)
K.C. Das, I. Gutman, On Sombor index of trees. Appl. Math. Comput. 412, 126575 (2022)
K.C. Das, A.S. Çevik, I.N. Cangul, Y. Shang, On Sombor index. Symmetry 13(1), 140 (2021)
K.C. Das, Y. Shang, Some extremal graphs with respect to Sombor index. Mathematics 9(11), 1202 (2021)
R. Cruz, I. Gutman, J. Rada, Sombor index of chemical graphs. Appl. Math. Comput. 399, 126018 (2021)
H. Deng, Z. Tang, R. Wu, Molecular trees with extremal values of Sombor indices. Int. J. Quantum Chem. 121(11), 26622 (2021)
N. Ghanbari, S. Alikhani, Sombor index of certain graphs. arXiv preprint (2021). arXiv:2102.10409
N.J.M.M. Raja, A. Anuradha, On Sombor indices of generalized tensor product of graph families. Results Control Optim. 14, 100375 (2024)
R. Cruz, J. Rada, Extremal values of the Sombor index in unicyclic and bicyclic graphs. J. Math. Chem. 59, 1098–1116 (2021)
J.-B. Liu, Y.-Q. Zheng, X.-B. Peng, The statistical analysis for Sombor indices in a random polygonal chain networks. Discret. Appl. Math. 338, 218–233 (2023)
V. Kulli, Neighborhood Sombor index of some nanostructures. Int. J. Math. Trends Technol. 67(5), 101–108 (2021)
J. Rada, J.M. Rodríguez, J.M. Sigarreta, General properties on Sombor indices. Discret. Appl. Math. 299, 87–97 (2021)
T. Radhakrishnan, W. Herndon, Molar volumes of alkanes and topological indices. J. Math. Chem. 2(4), 391–399 (1988)
J.-B. Liu, D.A. Xavier, E.S. Varghese, A. Baby, D. Mathew, Molecular descriptors of porphyrin-based dendrimer. Polycyclic Aromat. Compd. 43(7), 6126–6137 (2023)
J.-B. Liu, H. Iqbal, K. Shahzad, Topological properties of concealed non-Kekulean benzenoid hydrocarbon. Polycyclic Aromat. Compd. 43(2), 1776–1787 (2023)
S. Das, S. Rai, V. Kumar, On topological indices of Molnupiravir and its QSPR modelling with some other antiviral drugs to treat COVID-19 patients. J. Math. Chem. (2023). https://doi.org/10.1007/s10910-023-01518-z
X. Zuo, M.F. Nadeem, M.K. Siddiqui, M. Azeem, Edge weight based entropy of different topologies of carbon nanotubes. IEEE Access 9, 102019–102029 (2021)
P. Bustamante, S. Romero, A. Peña, B. Escalera, A. Reillo, Enthalpy–entropy compensation for the solubility of drugs in solvent mixtures: paracetamol, acetanilide, and nalidixic acid in dioxane-water. J. Pharm. Sci. 87(12), 1590–1596 (1998)
F. Prado-Prado, X. García-Mera, P. Abeijón, N. Alonso, O. Caamaño, M. Yáñez, T. Gárate, M. Mezo, M. González-Warleta, L. Muiño et al., Using entropy of drug and protein graphs to predict FDA drug-target network: theoretic-experimental study of MAO inhibitors and hemoglobin peptides from Fasciola hepatica. Eur. J. Med. Chem. 46(4), 1074–1094 (2011)
P.G. Seybold, M. May, U.A. Bagal, Molecular structure: property relationships. J. Chem. Educ. 64(7), 575 (1987)
R. Guha, D. Velegol, Harnessing Shannon entropy-based descriptors in machine learning models to enhance the prediction accuracy of molecular properties. J. Cheminform. 15(1), 1–11 (2023)
M.D. Vale Cunha, C.C. Ribeiro Santos, M.A. Moret, H.B. Barros Pereira, Shannon entropy in time-varying semantic networks of titles of scientific paper. Appl. Netw. Sci. 5(1), 53 (2020)
W. Gao, M. Imran, A.Q. Baig, H. Ali, M.R. Farahani, Computing topological indices of sudoku graphs. J. Appl. Math. Comput. 55, 99–117 (2017)
S.C. Basak, G.J. Niemi, G.D. Veith, Predicting properties of molecules using graph invariants. J. Math. Chem. 7(1), 243–272 (1991)
S. Hosamani, D. Perigidad, S. Jamagoud, Y. Maled, S. Gavade, QSPR analysis of certain degree based topological indices. J. Stat. Appl. Probab. 6(2), 361–371 (2017)
N.J.M.M. Raja, A. Anuradha, Topological entropies of single walled carbon nanotubes. J. Math. Chem. (2023). https://doi.org/10.1007/s10910-023-01532-1
S. Chatterjee, B. Price, Regression Diagnostics (Wiley, New York, 1991)
S. Das, S. Chatterjee, Multicollinearity problem—root cause, diagnostics and way outs. Diagnostics and Way Outs, 29 April 2011
J. Jacob, R. Varadharajan, Simultaneous raise regression: a novel approach to combating collinearity in linear regression models. Qual. Quant. 57(5), 4365–4386 (2023)
J. Neter, W. Wasserman, M.H. Kutner, Applied linear statistical models: regression. Anal. Var. Exp. Des. 1(985), 382–393 (1985)
K. Aarthi, S. Elumalai, S. Balachandran, S. Mondal, Extremal values of the atom-bond sum-connectivity index in bicyclic graphs. J. Appl. Math. Comput. 69(6), 4269–4285 (2023)
Acknowledgements
The corresponding author (A. Anuradha) would like to thank SRM Institute of Science and Technology, Tamil Nadu, India for supporting her research under the “Selective Excellence Research Initiative - 2021” grant.
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Nadar Jenita Mary Masilamani Raja and A. Anuradha have contributed equally to this work.
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Raja, N.J.M.M., Anuradha, A. Bonding alkane attributes with topological indices: a statistical intervention. J Math Chem (2024). https://doi.org/10.1007/s10910-024-01584-x
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DOI: https://doi.org/10.1007/s10910-024-01584-x