Quantum Hall effect and the topological number in graphene

The unconventional integer quantum Hall effect in graphene is shown to be due to the topological invariance. The quantized Hall conductivity is obtained to be odd integer, $\pm1, \pm3, \pm5, ...$ times two (spin degrees of freedom) when a uniform magnetic field is as high as 30T for example. However the quantization $\pm2, \pm4, \pm6, >...$ should be observed for higher magnetic field say 400T. When the system is anisotropic and described by the generalized honeycomb lattice, Hall conductivity is quantized to be any integer number.