Graph Entropy of Some Special Chemical Graphs
DOI:
https://doi.org/10.21123/bsj.2024.10258Keywords:
Alkane Isomers, Caterpillar Graph, Eigenvalue-based Modulus Entropy, Graph Energy, Graph SpectrumAbstract
Chemical graph theory plays an important role in modelling molecules, especially examining physico-chemical properties of the chemical compounds. Alkanes are one of the chemical compounds which are made up of hydrogen and carbon atoms, generally known as hydrocarbons. These alkanes having empirical formula . Structural/constitutional isomers are the collection of chemical compounds having same empirical formula but different structural arrangements, this lead to the diversity in the physico-chemical properties. Graph descriptors are the essential tools in the graph theory to study about these physico-chemical properties. Some of these graph descriptors are graph spectrum, graph energy and graph entropy which contribute significantly to understand molecular properties. Spectral parameters, like spectral radius, second largest eigenvalue, spectral gap and graph energy aid in estimating energy levels and stability of the molecule, while graph entropy, such as eigenvalue-based modulus entropy derived from the adjacency matrix, measure heterogeneity. This paper explores a specific type of alkanes and their isomers, examining their spectral parameters and graph entropy. Through comparative graph plots, the nature of these parameters are observed, which sheds light on the molecular behaviours. This study shows the importance of graph theory in quantum chemistry, particularly the spectral characteristics and structural intricacies of alkanes and their isomers, contributing to a comprehensive understanding of molecular properties and behaviour at the quantum level.
Received 21/11/2023
Revised 28/04/2024
Accepted 30/04/2024
Published Online First 20/06/2024
References
Wagner, Stephan, Hua Wang. Introduction to Chemical Graph Theory. Florida: CRC Press Taylor & Francis Group; 2018 Sep 5. p. 1-10. https://doi.org/10.1201/9780429450532.
Sun Y, Zhao H. Eigenvalue-based entropy and spectrum of bipartite digraph. Complex Intell Syst. 2022 Sep 20; 8(4): 3451–3462. https://doi.org/10.1007/s40747-022-00679-9.
Balakrishnan R, Ranganathan K A Textbook of Graph Theory. 2nd Ed. New York Heidelberg Dordrecht London: Springer Science & Business Media; 2012. p. 261-267. https://doi.org/10.1007/978-1-4614-4529-6.
Dehmer M. Information processing in complex networks: Graph entropy and information functionals. Appl Math Comput. 2008 Jul 15; 201(1-2): 82–94. https://doi.org/10.1016/j.amc.2007.12.010.
Brouwer AE, Haemers WH. Spectra of Graphs. New York Heidelberg Dordrecht London: Springer Science & Business Media Springer; 2011 Dec 17. p. 1-17. https://doi.org/10.1007/978-1-4614-1939-6_1.
Celik F, Cangül İ. On the spectra of cycles and paths. TWMS J Appl Eng Math. 2019 Jul 1; 9(3): 571–580.
Alwan NA, Al-Saidi NM. A general formula for characteristic polynomials of some special graphs. Eng. & Tech J. 2016 May 1; 34(5): 638–650.
Gutman I, Trinajstić N. Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons. Chem Phys Lett. 1972 Dec 15; 17(4): 535–538. https://doi.org/10.1016/0009-2614(72)85099-1.
Anwar S, Jamil MK, Alali AS, Zegham M, Javed A. Extremal values of the first reformulated Zagreb index for molecular trees with application to octane isomers. AIMS Math 2024; 9(1): 289-301. http://dx.doi.org/10.3934/math.2024017.
Mitesh JP, Kajal SB, Ashika .P. More on second Zagreb energy of graphs. Open J Discret Appl Math. 2023 Dec 27. 2(4): 7 – 13. http://dx.doi.org/10.30538/psrp-odam2023.0084.
Dobrynin AA, Estaji E. Wiener index of hexagonal chains under some transformations. Open J Discret Appl Math. 2020 Dec 31; 3(1): 28-36. https://doi:10.30538/psrp-odam2020.0027.
Noor M, Jamil MK, Ullah K, Azeem M, Pamucar D, Almohsen B. Energies of T-spherical fuzzy graph based on novel Aczel-Alsina T-norm and T-conorm with their applications in decision making. J Intell Fuzzy Syst. 2023 Jan 1. 45(6): 9363 – 9385. http://dx.doi.org/ 10.3233/JIFS-231086.
Waheed M, Saleem U, Javed A, Jamil MK. Computational aspects of entropy measures for metal organic frameworks. Mol Phys. 2023 Sep 7: e2254418. https://doi.org/10.3390/molecules28124726 .
Al-Janabi H, Bacs´o G. Sanskruti Index of some Chemical Trees and Unicyclic Graphs. J Phys Conf Ser. 2022 Jun 1; 2287: 012005. https://doi.org/10.1088/1742-6596/2287/1/012005 .
Lin Z. Connectivity indices and QSPR analysis of benzenoid hydrocarbons. Open J Discret Appl Math. 2023 Dec 27. 3(2): 35 – 40. https://doi.org/10.30538/psrp-odam2023.0092 .
Ahmad Z, Naseem M, Jamil MK, Siddiquid MK, Nadeemd MF. New results on eccentric connectivity indices of V-Phenylenic nanotube. Eurasian Chem Commun. 2020 June 1; 6(3): 663-71. http://dx.doi.org/10.33945/SAMI/ECC.2020.6.3
Raja NJMM, Anuradha A. Topological entropies of single walled carbon nanotubes. J. Math. Chem. 2023 Nov 2: 1-0. https://doi.org/10.1007/s10910-023-01532-1
Raja NJMM, Anuradha A. On Sombor indices of generalized tensor product of graph families. Results Control Optim. 2024 Jan 10: 100375. https://doi.org/10.1016/j.rico.2024.100375 .
Devaragudi V, Chaluvaraju B. Block Sombor index of a graph and its matrix representation. Open J Discret Appl Math. 2023 Apri 30; 6(1): 1-11. http://dx.doi.org/10.30538/psrp-odam2023.0078.
Jamil MK, Imran M, Abdul Sattar K. Novel face index for benzenoid hydrocarbons. Mathematics. 2020 Mar 1; 8(3): 312. http://dx.doi.org/doi:10.3390/math8030312.
Zhang X, Waheed M, Jamil MK, Saleemd U, Javed A. Entropy measures of the metal–organic network via topological descriptors. Main Group Met Chem. 2023 Dec 12; 46(1): 20230011. https://doi.org/10.1515/mgmc-2023-0011 .
Sardar MS, Siddique I, Jarad F, Ali MA, Türkan EM, Danish, M. Computation of vertex-based topological indices of middle graph of alkane. J Math. 2022; 2022(3): 24. https://doi.org/10.1155/2022/8283898 .
Sardar M S, Ali M A, Farahani M R, Alaeiyan M, Cancan M. Degree-based topological indices of alkanes by applying some graph operations. Eur Chem Bull. 2023; 12(5): 39-50. https://doi.org/10.31838/ecb/2023.12.si5.004 .
Puruchothama MN, Simon F. Diagrammatic representation between topological indices and alkanes. J Algebr Stat. 2022 Jul 23; 13(2): 3536–3545.
Lakshmi KV, Parvathi N. An analysis of thorn graph on topological indices. IAENG Int J Appl Math. 2023 Sep 1; 53(3): 1084-1093.
Javaid M, Siddique MK, Bonyah E. Computing Gutman connection index of thorn graphs. J Math. 2021 Nov 15; 2021(6): 11. https://doi.org/10.1155/2021/2289514 .
Chithra KP, Mayamma J. Total global dominator coloring of trees and unicyclic graphs. Baghdad Sci J. 2023; 20(4): 1380-1386. https://doi.org/10.21123/bsj.2023.6457 .
Ali AM, Ahmed HJ, Saleh GAM. Detour polynomials of generalized vertex identified of graphs. Baghdad Sci J. 2023 Apr 1; 20(2): 0343–0343. https://doi.org/10.21123/bsj.2022.6350 .
Ouellette RJ, Rawn JD. Organic Chemistry: Structure, Mechanism, Synthesis. Academic Press; 2018 Feb 3. p 87-133. https://doi.org/10.1016/C2016-0-04004-4 .
Clark GJ, Cooper JN. A Harary-Sachs theorem for hypergraphs. J Comb Theory Ser B. 2021 Jul 1; 149(1): 1–15. https://doi.org/10.1016/j.jctb.2021.01.002 .
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