Abstract
Chemical graph theory (CGT) is a field of mathematical chemistry focused on the study of molecules by applying classic graph theory. CGT studies molecules as graphs in which atoms are assumed to be vertices and bonds are taken as edges of graphs. In CGT, topological descriptors predict the physical and chemical properties of any molecular structure. In this paper, we computed some novel topological descriptors viz. Modified version of the Second Zagreb index, Hyper index, Randić index, Modified version of the Forgotten topological index and redefined third Zagreb index for cerium oxide nanostructures (\({\text{CeO}}_{2}[\alpha ,\beta ,\gamma ]\)) with \(\alpha \times\upbeta\) unit cell and \(\gamma\) layers. Based on the derived formulas, we compared the numerical results and physio-chemical properties of the under study\({\text{CeO}}_{2}[\alpha ,\beta ,\gamma ]\).
Similar content being viewed by others
Data availability
Not applicable.
Code availability
Not applicable.
References
Bonchev D (2001) Overall connectivity—a next generation molecular connectivity. J Mol Graph Model 20:65–75
Chu Y-M, Siddiqui MK, Javed S, Sherin L, Kausar F (2022) On zagreb type molecular descriptors of ceria oxide and their applications. J Cluster Sci 33:537–546
Došlić T (2008) Vertex-weighted Wiener polynomials for composite graphs. Ars Math Contem 1:66–80
Fajtlowicz S (1987) On conjectures of Graffiti-II. Congr Numer 60:187–197
Kanwal S, Shang S, Siddiqui MK, Shaikh TS, Afzal A, Asare-Tuah A (2021) On analysis of topological aspects for subdivision of kragujevac tree networks. Math Prob Eng 2021:1–15. https://doi.org/10.1155/2021/9082320
Manzoor S, Siddiqui MK, Ahmad S (2020) On entropy measures of molecular graphs using topological indices. Arab J Chem 13:6285–6298
Manzoor S, Siddiqui MK, Ahmad S (2022) Computation of entropy measures for phthalocyanines and porphyrins dendrimers. Int J Quan Chem 122:e26854
Ornatska M, Sharpe E, Andreescu D, Andreescu S (2011) Paper bioassay based on ceria nanoparticles as colorimetric probes. Anal Chem 83:4273–4280
Randic M (1975) Characterization of molecular branching. J Am Chem Soc 97:6609–6615
Siddiqui MK, Imran M, Ahmad A (2016) On Zagreb indices. Zagreb Polynomials of Some Nanostar Dendrimers. Appl Math Comput 280:132–139
Siddiqui MK, Chu Y-M, Nasir M, Nadeem MF, Hanif MF (2021) On topological descriptors of ceria oxide and their applications. J Main Group Metal Chem 44:103–116
Tsunekawa S, Sivamohan R, Ito S, Kasuya A, Fukuda T (1999) Structural study on monosize CeO2-x nano-particles. Nanostruct Mater 11:141–147
Ullah A, Zeb A, Zaman S (2022a) A new perspective on the modeling and topological characterization of H-Naphtalenic nanosheets with applications. J Mol Model 28:1–13
Ullah A, Qasim M, Zaman S, Khan A (2022b) Computational and comparative aspects of two carbon nanosheets with respect to some novel topological indices. Ain Shams Eng J 13:101672
Vashistha I, Rohilla S (2020) Structural characterization and rietveld refinement of CeO2/CoFe2O4 nanocomposites prepared via coprecipitation method, IOP Conference Series: Materials Science and Engineering. IOP Publishing, Bristol, pp 012170
Wang G, Yan L, Zaman S, Zhang M (2020) The connective eccentricity index of graphs and its applications to octane isomers and benzenoid hydrocarbons. Int J Quantum Chem 120:e26334
Xu K, Das KC, Tang K (2013) On the multiplicative Zagreb coindex of graphs. Opuscula Math 33:191–204
Zaman S, Ali A (2021) On connected graphs having the maximum connective eccentricity index. J Appl Math Comput 67:131–142
Zaman S, He X (2022) Relation between the inertia indices of a complex unit gain graph and those of its underlying graph. Linear Multilinear Algebra 70:843–877.
Zaman S, Jalani M, Ullah A, Saeedi G (2022) Structural analysis and topological characterization of sudoku nanosheet. J Math 2022:1–10. https://doi.org/10.1155/2022/5915740
Zhang Q, Munir MM, Ahmad H, Liu J-B (2022) Irregularity molecular descriptors of Cerium oxide CeO2 based on mathematical model and calculation. J Arab Chem 15:103567
Funding
The author Asad Ullah gratefully acknowledges the financial support for this study derived from the Higher Education Commission of Pakistan (Grant No. 20–11682/NRPU/R&D/HEC/2020).
Author information
Authors and Affiliations
Contributions
All have equally subsidized to this paper in all steps, from conceptualization to the write-up of final draft.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no any conflict of interest/competing interests.
Ethics approval and consent to participate
Not applicable.
Consent for publication
All authors have approved the manuscript and given consent for publication.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zaman, S., Jalani, M., Ullah, A. et al. On the topological descriptors and structural analysis of cerium oxide nanostructures. Chem. Pap. 77, 2917–2922 (2023). https://doi.org/10.1007/s11696-023-02675-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11696-023-02675-w