  According to the tight-binding approximation, we investigate the electronic
structures of graphene ribbons with zigzag shaped edges (ZGRs) and armchair
shaped edges (AGRs) drawn by the tensile force, and obtain the analytic
relations between the energy bands of pi-electrons in ZGR, AGR and the tensile
force based on only considering the nearest-neighbor interaction and the
hydrogen-like atomic wave function is considered as pi-electron wave function.
Importantly, we find the tensile force can open an energy gap at the K point
for ZGR and AGR, and the force perpendicular to the zigzag edges can open
energy gap more easily besides the gap values of ZGR and AGR at the K point
both increase as the tensile force increases.
