On the Gutman-Milovanović index and chemical applications

Edil D. Molina; José M. Rodríguez-García; José M. Sigarreta; Sergio J. Torralbas Fitz; Edil D. Molina; José M. Rodríguez-García; José M. Sigarreta; Sergio J. Torralbas Fitz

doi:10.3934/math.2025094

AIMS Mathematics

2025, Volume 10, Issue 2: 1998-2020. doi: 10.3934/math.2025094

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On the Gutman-Milovanović index and chemical applications

1.
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco, Guerrero, México
2.
Universidad Carlos Ⅲ de Madrid, ROR: https://ror.org/03ths8210, Departamento de Matemáticas, Avenida de la Universidad, 30 (edificio Sabatini), 28911 Leganés (Madrid), Spain
3.
Biostatistician - Musculoskeletal Oncology Division, Miller School of Medicine, University of Miami, Florida, USA

Received: 11 December 2024 Revised: 15 January 2025 Accepted: 20 January 2025 Published: 07 February 2025
MSC : 05C09, 05C92, 92E10

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.
- Gutman-Milovanović index,
- variable topological indices,
- general Zagreb indices,
- general sum-connectivity index,
- vertex-degree-based topological indices
Citation: Edil D. Molina, José M. Rodríguez-García, José M. Sigarreta, Sergio J. Torralbas Fitz. On the Gutman-Milovanović index and chemical applications[J]. AIMS Mathematics, 2025, 10(2): 1998-2020. doi: 10.3934/math.2025094

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Abstract

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.

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