(untitled) (Contemporary Mathematics, 2025)
Recently, graphene has become a significant and interesting substance. Many researchers have studied graphene-related materials in extensive detail both theoretically and practically, drawn by its exceptional features. The collection of graphene-bound materials that contain in-plane nanopores is called porous graphene, which exhibits structural and electrochemical properties distinct from pure ones. Porous graphene large surface area and excellent conductivity render it optimal for battery and supercapacitor energy retention biosensors, DNA sequencing, hydrogen storage and gas separation. Where Omega, Sadhana, and PI polynomials optimize charge distribution and energy density for better performance in devices like electric vehicles and smartphones. The present work concentrates on obtaining the polynomials Omega, Sadhana, and PI that are based on quasi-orthogonal cuts which are related to certain properties and express graph topological invariants.