Exploring extremal molecular characteristics: insights from nanosheets and polycyclic aromatic hydrocarbons

In this work, we applied neighborhood degree sum-based indices to explore extremal molecular characteristics. We reveal distinct extremal behaviors in molecular graphs by studying two nanosheet structures, \(T^2C_4C_8(R)\) $T^2{C}_4{C}_8(R)$ and \(T^1C_4C_8(S)\) $T^1{C}_4{C}_8(S)$ , and polycyclic aromatic hydrocarbon \(PAH_s\) $PA{H}_s$ . The application is extended to carbon nanotubes (CNTs), where their scientific uses heavily rely on their extremal features. We reveal extreme molecular properties of polycyclic aromatic hydrocarbons (PAHs) through computational evaluations, with implications for environmental and health research. This work provides a thorough grasp of the relevance of extremal molecular properties in a variety of molecular configurations.