Topological and entropic characterization of nitrogenated holey graphene

Nitrogenated holey graphene (NHG), a two-dimensional (2D) carbon nanomaterial, demonstrates exceptional electrical, thermal, and chemical characteristics owing to its inherent porosity and nitrogen doping. This study examines the structural and informational properties of NHG by calculating various degree-based topological indices in conjunction with Shannon entropy metrics. Two unique pore geometries-hexagonal, triangular and parallelogram are represented as molecular graphs. To statistically confirm the descriptors, we conduct regression analysis correlating algebraic structure count, resonance energy, and entropy measurements, revealing robust predictive connections. Our findings indicate that pore geometry markedly affects connection patterns, resulting in unique entropy signatures and structural responses. These insights statistically delineate the complexity of NHG and provide a basis for forecasting structure-property interactions, hence facilitating the rational design of NHG-based nanodevices with customised functionality.