Sulfuric acid mainly intercalates into graphite layers and also helps to form diamanganese heptoxide (Mn2O7) when potassium permanganate reacts with sulfuric acid. This Mn2O7 is the active oxidizing species for graphite oxidation.
Sodium nitrate further enhances the oxidation on the basal plane of graphitic sheets
Hydrogen peroxide is used to remove/neutralize the potassium permanganate from the reaction system.