  The geometrical, electronic, and magnetic properties of twisted zigzag-edged
graphene nanoribbons (ZGNRs) and novel graphene M\"obius strips (GMS) are
systematically investigated using first-principles density functional
calculations. The structures of ZGNRs and GMS are optimized, and their
stabilities are examined. The molecular energy levels and the spin polarized
density of states are calculated. It is found that for twisted ZGNRs, the
atomic bonding energy decreases quadratically with the increase of the twisted
angle, and the HOMO-LUMO gap are varying in a sine-like behavior with the
twisted angle. The calculated spin densities reveal that the ZGNRs and GMS have
antiferromagnetic ground states, which persist during the twisting. The spin
flips on the zigzag edges of GMS are observed at some positions.
