On the Gutman-Milovanović index and chemical applications
The determination of upper and lower bounds for topological indices in molecular graphs provides critical insights into the structural properties of chemical compounds. These bounds facilitate the estimation of the ranges of topological indices based on molecular structural parameters. This study pr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025094 |
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| author | Edil D. Molina José M. Rodríguez-García José M. Sigarreta Sergio J. Torralbas Fitz |
| author_facet | Edil D. Molina José M. Rodríguez-García José M. Sigarreta Sergio J. Torralbas Fitz |
| author_sort | Edil D. Molina |
| collection | DOAJ |
| description | The determination of upper and lower bounds for topological indices in molecular graphs provides critical insights into the structural properties of chemical compounds. These bounds facilitate the estimation of the ranges of topological indices based on molecular structural parameters. This study presents novel inequalities for the Gutman-Milovanović index, which generalizes several significant indices such as the first and second Zagreb indices, the Randić index, the harmonic index, the geometric-arithmetic index, the general second Zagreb index, and the general sum-connectivity index. Moreover, we derive and characterize extremal graphs for many of these inequalities. Additionally, we explore the application of the Gutman-Milovanović index in modeling the physicochemical properties of 22 polycyclic aromatic hydrocarbons. Our results demonstrate that the topological index $ M_{\alpha, \beta} $ provides accurate predictions for these properties, with $ R^2 $ values ranging from 0.9406 to 0.9983, indicating a strong correlation between the index and experimental data. The findings underscore the versatility of $ M_{\alpha, \beta} $ in chemical applications. |
| format | Article |
| id | doaj-art-86d7d37b00af4de3b006dacba3ad9eb8 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-86d7d37b00af4de3b006dacba3ad9eb82025-08-20T03:17:09ZengAIMS PressAIMS Mathematics2473-69882025-02-011021998202010.3934/math.2025094On the Gutman-Milovanović index and chemical applicationsEdil D. Molina0https://orcid.org/0000-0003-2620-0150José M. Rodríguez-García1https://orcid.org/0000-0003-2851-7442José M. Sigarreta2https://orcid.org/0000-0002-0863-4695Sergio J. Torralbas Fitz3https://orcid.org/0000-0002-0348-2143Facultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco, Guerrero, MéxicoUniversidad Carlos Ⅲ de Madrid, ROR: https://ror.org/03ths8210, Departamento de Matemáticas, Avenida de la Universidad, 30 (edificio Sabatini), 28911 Leganés (Madrid), SpainFacultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco, Guerrero, MéxicoBiostatistician - Musculoskeletal Oncology Division, Miller School of Medicine, University of Miami, Florida, USAThe determination of upper and lower bounds for topological indices in molecular graphs provides critical insights into the structural properties of chemical compounds. These bounds facilitate the estimation of the ranges of topological indices based on molecular structural parameters. This study presents novel inequalities for the Gutman-Milovanović index, which generalizes several significant indices such as the first and second Zagreb indices, the Randić index, the harmonic index, the geometric-arithmetic index, the general second Zagreb index, and the general sum-connectivity index. Moreover, we derive and characterize extremal graphs for many of these inequalities. Additionally, we explore the application of the Gutman-Milovanović index in modeling the physicochemical properties of 22 polycyclic aromatic hydrocarbons. Our results demonstrate that the topological index $ M_{\alpha, \beta} $ provides accurate predictions for these properties, with $ R^2 $ values ranging from 0.9406 to 0.9983, indicating a strong correlation between the index and experimental data. The findings underscore the versatility of $ M_{\alpha, \beta} $ in chemical applications.https://www.aimspress.com/article/doi/10.3934/math.2025094gutman-milovanović indexvariable topological indicesgeneral zagreb indicesgeneral sum-connectivity indexvertex-degree-based topological indices |
| spellingShingle | Edil D. Molina José M. Rodríguez-García José M. Sigarreta Sergio J. Torralbas Fitz On the Gutman-Milovanović index and chemical applications AIMS Mathematics gutman-milovanović index variable topological indices general zagreb indices general sum-connectivity index vertex-degree-based topological indices |
| title | On the Gutman-Milovanović index and chemical applications |
| title_full | On the Gutman-Milovanović index and chemical applications |
| title_fullStr | On the Gutman-Milovanović index and chemical applications |
| title_full_unstemmed | On the Gutman-Milovanović index and chemical applications |
| title_short | On the Gutman-Milovanović index and chemical applications |
| title_sort | on the gutman milovanovic index and chemical applications |
| topic | gutman-milovanović index variable topological indices general zagreb indices general sum-connectivity index vertex-degree-based topological indices |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025094 |
| work_keys_str_mv | AT edildmolina onthegutmanmilovanovicindexandchemicalapplications AT josemrodriguezgarcia onthegutmanmilovanovicindexandchemicalapplications AT josemsigarreta onthegutmanmilovanovicindexandchemicalapplications AT sergiojtorralbasfitz onthegutmanmilovanovicindexandchemicalapplications |