Graph spectral analysis of nonane isomers
https://doi.org/10.17586/2220-8054-2024-15-1-16-22
Abstract
A group of substances known as alkanes is made up of carbon and hydrogen atoms bound together only by single covalent bond with the chemical formula CnH2n+2. Isomers are those molecules with identical chemical formula but different structural arrangement. Due to this, their corresponding molecular graphs differ in structure thereby leading to distinct spectral parameters. In this work, the spectral parameters of all isomers of nonane C9H20 have been computed and its relationship with its eigenvalue-based entropy is established. The spectral results are then correlated with the density value of the nonane isomers and it is found that the “spectral gap” is closely associated to that of density.
About the Authors
B. I. AndrewIndia
Barnabas I. Andrew – Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology.
Kattankulathur, Tamil Nadu 603203
A. Anuradha
India
Ambarishan Anuradha – Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology.
Kattankulathur, Tamil Nadu 603203
References
1. Arora A. Hydrocarbons (Alkanes, Alkenes and Alkynes) Discovery Publishing House, 2006.
2. Balaban A.T. Applications of graph theory in chemistry. Journal of chemical information and computer sciences, 1985, 25(3), P. 334–343.
3. Dehmer M., Emmert-Streib F., Chen Z., Li X., Shi Y. eds. Mathematical Foundations and Applications of Graph Entropy. John Wiley & Sons, 2017.
4. Asuero A.G., Sayago A. and Gonza´lez A.G. The correlation coefficient: An overview. Critical Reviews in Analytical Chemistry, 2006, 36(1), P. 41–59.
5. Berkolaiko G., Kuchment P., Introduction to Quantum Graphs. American Mathematical Soc. Providence, 2013.
6. Blinova I.V., Popov A.I. and Bosova A.A. Spectral gaps for star-like quantum graph and for two coupled rings. Nanosystems: Phys. Chem. Math., 2022, 13(3), P. 245–249.
7. Balakrishnan R., Ranganathan K. A Textbook of Graph Theory. Springer Science & Business Media, 2012.
8. Sun Y. and Zhao H. Eigenvalue-based entropy and spectrum of bipartite digraph. Complex & Intelligent Systems, 2022, 8(4), P. 3451–3462.
9. Jerrold H.Z. Spearman rank correlation. Encyclopedia of biostatistics, 2005, 7.
10. Brouwer A.E., Haemers W.H. Spectra of Graphs. Springer Science & Business Media, 2011.
11. Spielman D.A. Spectral graph theory and its applications. In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS’07), IEEE, 2007, P. 29–38.
12. Gutman I., Trinajstic´ N. Graph theory and molecular orbitals. total ϕ-electron energy of alternant hydrocarbons. Chemical Physics Letters, 1972, 17(4), P. 535–538.
13. Harary F., Schwenk A.J. Which graphs have integral spectra? In Graphs and Combinatorics: Proceedings of the Capital Conference on Graph Theory and Combinatorics at the George Washington University June, 1973, P. 18–22.
14. Ahmadi O., Alon N., Blake I.F. and Shparlinski I.E. Graphs with integral spectrum Linear Algebra and its Applications, 2009, 430(1), P. 547–552.
15. Indulal G., Balakrishnan R., Anuradha A. Some new families of integral graphs. Indian Journal of Pure and Applied Mathematics, 2014, 45(6), P. 805–817.
16. Dehmer M. and Mowshowitz A. A history of graph entropy measures. Information Sciences, 2011, 181(1), P. 57–78.
17. Dehmer M. Information processing in complex networks: Graph entropy and information functionals. Applied Mathematics and Computation, 2008, 201(1-2), P. 82–94.
18. Rodr´ıguez-Vela´zquez J.A. and Balaban A.T. Two new topological indices based on graph adjacency matrix eigenvalues and eigenvectors. Journal of Mathematical Chemistry, 2019, 57, P. 1053–1074.
19. Puth M.T., Neuha¨user M., Ruxton G.D. Effective use of pearson’s product–moment correlation coefficient. Animal Behaviour, 2014, 430(1), P. 183–189.
20. C. Book. N-decane basic information, 2023. URL/arXiv: https://www.chemicalbook.com/ProductChemicalPropertiesCB6392378EN.htm
Review
For citations:
Andrew B.I., Anuradha A. Graph spectral analysis of nonane isomers. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(1):16-22. https://doi.org/10.17586/2220-8054-2024-15-1-16-22