We have studied numerically the mesoscopic fluctuations of the conductance of a graphene strip (width W larger than length L), in an ensemble of samples with different realizations of the random electrostatic potential landscape. For strong disorder (potential fluctuations comparable to the hopping energy), the variance of the conductance approximates the value predicted by the Altshuler-Lee-Stone theory of universal conductance fluctuations, Var GUCF=0.12 (W/L)(2e2/h)2. For weaker disorder the variance is greatly enhanced if the potential is smooth on the scale of the atomic separation. There is no enhancement if the potential varies on the atomic scale, indicating that the absence of backscattering on the honeycomb lattice is at the origin of the anomalously large fluctuations.
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