In this work, we employ a graph-theoretical framework to study the structural characteristics of nanocarbon sheets. Key auxiliary properties are predicted using the Van, R, and S topological indices, which makes it easier to design materials that are both energy-efficient and environmentally friendly. The analysis assesses how topological characteristics can affect performance metrics that are important for long-term uses in green energy systems. Our results show how useful these descriptors are for simulating the behavior of sustainable nanomaterials based on nanocarbons and directing the creation of devices with lower power consumption and higher energy efficiency. Theoretical expressions are clearly visualized by the use of tables and three-dimensional MATLAB figures.