  The variable range hopping theory, as formulated for exponentially localized
impurity states, does not necessarily apply in the case of graphene with
covalently attached impurities. We analyze the localization of impurity states
in graphene using the nearest-neighbor, tight-binding model of an
adatom-graphene system with Green's function perturbation methods. The
amplitude of the impurity state wave function is determined to decay as a power
law with exponents depending on sublattice, direction, and the impurity
species. We revisit the variable range hopping theory in view of this result
and find that the conductivity depends as a power law of the temperature with
an exponent related to the localization of the wave function. We show that this
temperature dependence is in agreement with available experimental results.
