We present a detailed analysis of the factors influencing the formation of epoxide and ether groups in graphene nanoflakes using conventional density functional theory (DFT), the density-functional tight-binding (DFTB) method, π-Hückel theory, and graph theoretical invariants. The relative thermodynamic stability associated with the chemisorption of oxygen atoms at various positions on hexagonal graphene flakes (HGFs) of D6h-symmetry is determined by two factors-viz. The disruption of the π-conjugation of the HGF and the geometrical deformation of the HGF structure. The thermodynamically most stable structure is achieved when the former factor is minimized, and the latter factor is simultaneously maximized. Infrared (IR) spectra computed using DFT and DFTB reveal a close correlation between the relative thermodynamic stabilities of the oxidized HGF structures and their IR spectral activities. The most stable oxidized structures exhibit significant IR activity between 600 and 1800 cm-1, whereas less stable oxidized structures exhibit little to no activity in this region. In contrast, Raman spectra are found to be less informative in this respect.