Role of GA, AG and R in Structure-Property Modelling

Molecular descriptors are essential tools that bridge the gap between chemical structures and their properties. Among these, the Randić index (R), geometric-arithmetic index (GA), and arithmetic-geometric index (AG) are well-established. However, the relationships between these descriptors, particularly the gaps $\text{GA}-R$ and $\text{AG}-R,$ have not been extensively explored. This study investigates the impact of these descriptor gaps on chemical graph theory. Our findings reveal that the differences $\text{GA}-R$ and $\text{AG}-R$ provide unique insights into the structure-property modeling of molecules, particularly outperforming AG, GA, R, and other known descriptors for alkanes. Polycyclic aromatic compounds (PACs) are organic molecules composed of multiple fused aromatic rings. PACs are of significant environmental concern due to their persistence and potential toxicity, including carcinogenic properties. The effectiveness of $\text{GA}-R$ and $\text{AG}-R$ is observed to be strong in structure-property modeling for some polycyclic aromatic compounds. Additionally, $\text{GA}-R$ and $\text{AG}-R$ are recognized as important descriptors for various pharmaceutical compounds employed in treating malignant diseases.