Abstract: Graphene is the latest allotrope of carbon to be under the spotlight ever since its discovery by Novoselov and coworkers in 2004. Owing to its fascinating structural, electrical, optical, mechanical and thermal properties, graphene can be regarded as as a rapidly rising star in various fields such as supercapacitors, biosensors and batteries. The organic chemistry of graphene has stimulated a great deal of research and is gaining considerable attention. Among the various experimental studies which have been carried out on graphene, it is found that [3+2] cycloadditions (32CA) can also be achieved on graphene sheets and the resulting functionalized graphenes are dispersible in polar organic solvents and water. The outstanding properties of graphene inspire fundamental studies and within the context of our recent publication on the 32CA of nitrile oxides with fullerene, we now explore the 32CA of unsubstituted (HCNO) and substituted nitrile oxides (FCNO and MeCNO) to model of graphenes. We seek to rationalize the energetic, thermodynamic and kinetic parameters of these reactions. To the best of our knowledge this is the first time that transition states structure (TS) for 1,3-DC on graphene models have been reported. Our interest lies in gaining a better insight into the reaction mechanism such as its synchronicity, the nature of the TS, charge transfer, analysis of the reactivity indices and the rate constants. An unexpected behaviour (lowest activation energy) has been observed for the 32CA involving FCNO as these reactions have some pseudodiradical character. The findings of our research should be helpful to experimentalists in their quests for functionalized graphenes.