Chemical Graph Theory: Analyzing Molecular Properties Using Topological Indices

References

[1] Balaban, A. T. (2022). Chemical graph theory and topological indices: Applications in molecular modeling. Journal of Chemical Information and Modeling, 62(4), 1458–1473. https://doi.org/10.1021/acs.jcim.2c00035

[2] Balaban, A. T., & Ivanciuc, O. (2000). Historical development of topological indices. In A. T. Balaban & O. Ivanciuc (Eds.), Topological indices and related descriptors in QSAR and QSPR (pp. 31-68). CRC Press.

[3] Basak, S. C., Magnuson, V. R., Niemi, G. J., Regal, R. R., & Veith, G. D. (1987). Topological indices: their nature, mutual relatedness, and applications. Mathematical Modelling, 8, 300-305.

[4] Brezovnik, S., & Tratnik, N. (2022). General cut method for computing Szeged‐like topological indices with applications to molecular graphs. International Journal of Quantum Chemistry

[5] Bonchev, D., & Rouvray, D. H. (2021). Chemical graph theory: Introduction and applications. Mathematical Chemistry Reviews, 7(2), 201–225. https://doi.org/10.1016/j.mathchem.2021.04.012

[6] Chandrasekaran, S., & Swaminathan, V. (2023). Topological indices in computational drug discovery and cheminformatics. Journal of Molecular Graphics and Modelling, 118, 108–122. https://doi.org/10.1016/j.jmgm.2023.108122

[7] Das, P., Singh, R., & Bhattacharjee, D. (2023). Topological indices in QSPR and QSAR: A mathematical approach to molecular properties. Journal of Mathematical Chemistry, 61(2), 289–307. https://doi.org/10.1007/s10910-023-01234-9

[8] Diudea, M. V. (2019). Molecular topology and its applications in chemistry and biology. Computational Chemistry Reviews, 5(1), 145–172. https://doi.org/10.1016/j.ccrev.2019.01.004

[9] Estrada, E., Patlewicz, G., & Uriarte, E. (1998). From molecular graphs to drugs. A review on the use of topological indices in drug design and discovery. Indian Journal of Chemistry. Section A: Inorganic, Physical, Theoretical and Analytical Chemistry, 37(11), 849-864.

[10] Estrada, E. (2020). Graph theoretical approaches to chemical reactivity and molecular design. Chemical Society Reviews, 49(10), 3552–3580. https://doi.org/10.1039/C9CS00804H

[11] Gao, W., Wang, W., & Farahani, M. R. (2016). Topological indices study of molecular structure in anticancer drugs. Journal of chemistry, 2016(1), 3216327.

[12] Gutman, I., & Trinajstic, N. (1972). Graph theory and molecular orbitals. Chemical Physics Letters, 17(4), 535-538.

[13] Gutman, I., & Furtula, B. (2022). Recent advances in the theory of molecular structure descriptors. Mathematical Chemistry Monographs, 35, 98–123. https://doi.org/10.1007/s10910-022-01234-6

[14] Hameed, S., Jamil, M. K., Waheed, M., Azeem, M., & Swaray, S. (2022). Two complex graph operations and their exact formulations on topological properties. Complexity, 2022.

[15] Harary, F., & Palmer, E. M. (2020). Graphical enumeration and chemical graph theory applications. Springer Mathematics in Chemistry Series, 12, 213–234. https://doi.org/10.1007/978-3-030-46810-3_8

[16] Jerrum, M., & Sinclair, A. (1996). The Markov chain Monte Carlo method: An approach to approximate counting and integration. Approximation Algorithms for NP-hard Problems, 482-520.

[17] Jiang, Z., & Wang, X. (2024). Computational methods for predicting molecular properties using topological indices. Artificial Intelligence in Chemistry, 3, 108745. https://doi.org/10.1016/j.aiche.2024.108745

[18] Miličević, A., Nikolić, S., & Trinajstic, N. (2021). Comparative analysis of topological indices for molecular modeling. Croatica Chemica Acta, 94(3), 247–261. https://doi.org/10.5562/cca.2021.94.3.002

[19] Randic, M. (2019). The connectivity index: 40 years of development and applications in chemical graph theory. Journal of Mathematical Chemistry, 57(1), 151–172. https://doi.org/10.1007/s10910-019-01003-6

[20] Sarkar, P., De, N., & Buie, A. (2022). On some topological indices and their importance in chemical sciences: A comparative study. The European Physical Journal Plus, 137, 195. https://doi.org/10.1140/epjp/s13360-022-02312-0

[21] Schultz, H., & Wiener, H. (2023). Topological descriptors and their role in predicting physicochemical properties of molecules. Molecular Informatics, 42(6), e2200189. https://doi.org/10.1002/minf.202200189

[22] Todeschini, R., & Consonni, V. (2024). Handbook of molecular descriptors: Applications in drug design and materials science. Wiley-VCH. https://doi.org/10.1002/9783527699999

[23] Todeschini, R., & Consonni, V. (2000). Handbook of Molecular Descriptors. Wiley-VCH.

[24] Vasilyev, A., & Stevanović, D. (2014). MathChem: A Python package for calculating topological indices. MATCH Communications in Mathematical and in Computer Chemistry, 71(3), 657-680

[25] Vukicevic, D., & Furtula, B. (2021). Novel graph-based indices in predicting chemical properties. International Journal of Quantum Chemistry, 121(9), e26738. https://doi.org/10.1002/qua.26738

[26] Wardecki, D., Dołowy, M., & Bober-Majnusz, K. (2023). Evaluation of the usefulness of topological indices for predicting selected physicochemical properties of bioactive substances with anti-androgenic and hypouricemic activity. Molecules, 28(15), 5822.

[27] Wiener, H. (1947). Structural determination of paraffin boiling points. Journal of the American Chemical Society, 69(1), 17-20.

[28] Wiener, H. (2020). Structural determination of paraffin boiling points using topological methods. Journal of the American Chemical Society, 142(11), 4870–4882. https://doi.org/10.1021/jacs.0c01123

[29] Yirik, M. A., Çolpan, K. E., Schmidt, S., Sorokina, M., & Steinbeck, C. (2021). Review on Chemical Graph Theory and Its Application in Computer-Assisted Structure Elucidation. Preprints, 2021110546. https://doi.org/10.20944/preprints202111.0546.v1

[30] Zhou, X., & Li, Y. (2023). Advances in molecular topology and its applications in material science. Materials Chemistry Frontiers, 7(5), 2340–2352. https://doi.org/10.1039/D3MF00172H

@article{1707341,
      author = {Dr. Priyanka Y B},
      title = {Chemical Graph Theory: Analyzing Molecular Properties Using Topological Indices},
      journal = {Iconic Research And Engineering Journals},
      year = {2024},
      volume = {8},
      number = {4},
      pages = {793-803},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1707341.pdf},
      abstract = {Chemical graph theory utilizes mathematical graph concepts to model molecular structures, where atoms are represented as vertices and bonds as edges, enabling the analysis of molecular properties through topological indices numerical values derived from these graphs that correlate with various physicochemical and biological properties of compounds. These indices, such as the Wiener index, Zagreb indices, Randic connectivity index, and Sombor index, have been instrumental in predicting properties like boiling points, stability, and biological activity, thereby reducing the need for extensive laboratory experiments. The Wiener index, introduced in 1947, is based on the topological distance between vertices and was initially used to compare the boiling points of alkane isomers. Zagreb indices, first introduced in 1972, are based on the degrees of vertices and have been useful in modeling chemical and biological properties of compounds. The Randi? connectivity index, another well-known topological index, is calculated using the degrees of vertices and has been widely used in chemistry and pharmacology. The Sombor index, a more recent addition, is defined as the sum of the square roots of the sum of the squares of the degrees of pairs of adjacent vertices. These indices have been applied in quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) studies, providing insights into the relationship between molecular structure and properties. For instance, the Sombor index has been used to order chemical trees, unicyclic, bicyclic, and tricyclic graphs, aiding in the understanding of molecular stability and reactivity. Additionally, the study of k-distance degree-based topological indices, such as the leap and hyper leap Zagreb indices, has provided further understanding of the structural properties of benzenoid systems, which are important in organic chemistry. These advancements in chemical graph theory and the development of various topological indices have significantly contributed to the field of chemoinformatics, enabling the prediction of molecular properties and aiding in the design of new compounds with desired characteristics.},
      keywords = {Chemical Graph Theory, Topological Indices, Molecular Properties, Quantitative Structure-Property Relationship (QSPR), Quantitative Structure-Activity Relationship (QSAR), Chemoinformatics},
      month = {October},
  }