Topological characterization, entropy measures and prediction of properties of Iridium cored dendrimer

This study presents a comprehensive structural analysis of Iridium-cored dendrimers, denoted by $I_n\mathrm{mlr};n\ge 1$, with an emphasis on degree and distance based metrics to elucidate their structure-property relationships. Dendrimers, known for their highly branched architectures, are versatile macromolecules with applications across various scientific fields. In this work, molecular descriptors serve as essential numerical indicators, capturing bonding characteristics and aiding in the prediction of material properties. Leveraging a novel quotient graph approach, we compute a range of distance based indices, including the Wiener (W), Szeged (Sz and $S{z}_e$), Mostar (Mo and $M{o}_e$), and Padmakar-Ivan (PI) indices. We further derive generalized expressions for entropy measures associated with degree based indices, such as Shannon's entropy, providing a robust framework for assessing the structural complexity of these compounds. Additionally, we examine various degree based descriptors with entropy measures—including the Zagreb ($M_1$, $M_2$, and HM), Harmonic (H), Forgotten (F), Randic (R and RR), ABC, GA, SC, σ, and Irregularity indices (irr). A linear regression analysis is conducted to model dendrimer properties and forecast attributes for subsequent generations, potentially minimizing the need for extensive laboratory experimentation. Our findings provide valuable insights into the molecular intricacies of Iridium-cored dendrimers, bridging theoretical chemistry with practical applications and contributing to future advancements in materials science and engineering.