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Entire Irregularity Indices: A Comparative Analysis and Applications

Author

Listed:
  • Anwar Saleh

    (Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia)

  • Samirah Alsulami

    (Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia)

  • Maryam Alsulami

    (Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia)

Abstract

This research introduces two novel topological indices, the entire Albertson index and the entire sigma index, as quantitative measures of molecular irregularity. The indices are defined by precise mathematical formulas and their behavior is analyzed across a diverse range of graph families. To evaluate the predictive capabilities of the proposed indices, we compare their performance with established irregularity indices in the modeling of molecular properties. Correlations with physicochemical properties, including the boiling point, melting point, and molecular volume, are investigated. Specific expressions for these indices are derived for various molecular structures, such as bridge molecules, polyomino chains of n-cycles, triangular benzenoid graphs, graphene, and dendrimer stars D 3 [ n ] . The findings of this study contribute significantly to the field of chemical graph theory by providing novel tools to understand and predict molecular behavior. The entire irregularity indices have potential applications in drug discovery, materials science, and other areas where molecular properties are crucial.

Suggested Citation

  • Anwar Saleh & Samirah Alsulami & Maryam Alsulami, 2025. "Entire Irregularity Indices: A Comparative Analysis and Applications," Mathematics, MDPI, vol. 13(1), pages 1-30, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:146-:d:1559021
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    References listed on IDEAS

    as
    1. Slim Belhaiza & Nair Maria Maia Abreu & Pierre Hansen & Carla Silva Oliveira, 2005. "Variable Neighborhood Search for Extremal Graphs. XI. Bounds on Algebraic Connectivity," Springer Books, in: David Avis & Alain Hertz & Odile Marcotte (ed.), Graph Theory and Combinatorial Optimization, chapter 0, pages 1-16, Springer.
    2. Xiaolong Shi & Ruiqi Cai & Jaber Ramezani Tousi & Ali Asghar Talebi, 2024. "Quantitative Structure–Property Relationship Analysis in Molecular Graphs of Some Anticancer Drugs with Temperature Indices Approach," Mathematics, MDPI, vol. 12(13), pages 1-11, June.
    3. Sakander Hayat & Farwa Asmat, 2023. "Sharp Bounds on the Generalized Multiplicative First Zagreb Index of Graphs with Application to QSPR Modeling," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
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