Entire Irregularity Indices: A Comparative Analysis and Applications

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 D3[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.

Keywords

• entire Albertson index
• entire sigma index
• wheel graph
• helm graph
• tadpole graph