  We have investigated the low-frequency 1/f noise of both suspended and
on-substrate graphene field-effect transistors and its dependence on gate
voltage, in the temperature range between 300K and 30K. We have found that the
noise amplitude away from the Dirac point can be described by a generalized
Hooge's relation in which the Hooge parameter {\alpha}H is not constant but
decreases monotonically with the device's mobility, with a universal dependence
that is sample and temperature independent. The value of {\alpha}H is also
affected by the dynamics of disorder, which is not reflected in the DC
transport characteristics and varies with sample and temperature. We attribute
the diverse behavior of gate voltage dependence of the noise amplitude to the
relative contributions from various scattering mechanisms, and to potential
fluctuations near the Dirac point caused by charge carrier inhomogeneity. The
higher carrier mobility of suspended graphene devices accounts for values of
1/f noise significantly lower than those observed in on-substrate graphene
devices and most traditional electronic materials.
