The chemical bonding analysis using the adaptive natural density partitioning method of the C4F fluorinated graphene sheet revealed a chemical bonding model explaining its particular stability. We proposed that the stability of the C4F fluorinated graphene is due to the so-called "benzation" of graphene. On the basis of our chemical bonding model we predicted that other high-symmetry structures of the C7F4, C3F2, C13F10, etc. stoichiometries, containing planar hexagons, which are separated from each other by 2, 3, 4, etc. C-F fragments could also possess additional stability. We also suggested that other functionalized graphene structures of the C4X and C7X4, C3X2, C13X10 stoichiometries, where X is a monovalent atom (H, F, Cl) or a monovalent group (CN, CCH etc.), could also have extra stability. We hope that the developed model, obtained for the functionalization of pristine graphene, will give an impetus for experimentalists to devise methods, which could serve as useful tools for producing this kind of materials with the tailored properties.