stress[23]. Thus, in addition to H saturation, we have investigated possible edge reconstruc- tions in relieving the edge compressive stress. We have considered the Stone-Wales (SW) defect[24], which appealed to us become a SW defect in 2D is equivalent to a dislocation core in 3D that is known as a common stress relieve mechanism. Figure 4a shows the calculated armchair edge stress along with edge energy as a function of one type of SW defect (7-5-7 ring structure) concentration. Figure 4b shows an example of the optimized edge structure at the 50% defect concentration. One sees from Fig. 4a that the edge stress increases linearly from compressive to tensile with the increasing SW defect concentration. The most stable edge structure is at ∼ 25% defect concentration where the edge stress is very small and slightly compressive. A small stress value indicates that this chemically stable edge structure (with the lowest edge energy) is also most mechanically stable against deformation. Figure 5a shows the ground-state AF zigzag edge stress along with edge energy as a function of another type of SW defect (5-7 ring structure) concentration. Figure 5b shows an example of the optimized edge structure and spin charge density at the 50% defect concentration. Again, the edge stress increases linearly from compressive to tensile with the increasing defect concentration, the same as the case of armchair edge (Fig. 4a), but the edge energy decreases monotonically with the most stable edge having 100% of defects, in agreement with a recent first-principles calculation [8]. The initial compressive edge stress ( ∼ -0.5 eV/ ˚ A) is completely reversed to a large tensile value of ∼ 1.2 eV/ ˚ A in the most stable edge. Also, the 100% defected edge becomes non-spin-polarized. In general, the zigzag edge spin decreases continuously with the increasing SW defect concentration, similar to the behavior found previously for other types of defects [25]. We note that there is a first-principles calculation of graphene edge stress was reported recently[26], but that calculation appears inconsistent with all other existing first-principles calculations . Their edge energies differ from all previous results[8, 9] and ours that are consistent with each other. The well-known spin-polarization of the zigzag edge was not considered, the quantum oscillation of armchair edge energy and stress was not shown, and their edge stress were not calculated from direct quantum-mechanical formula [14]. In conclusion, quantum effects have been widely shown for electronic structure and ener- getic quantities of low-dimensional nanostructures. We demonstrate, in addition, quantum manifestations of mechanical quantities in graphene edge stress. We show that quantum confinement can lead to stress oscillations and spin polarization can reduce stress, which in 7