  Recently observed magnetophonon resonances in the magnetoresistance of
graphene are investigated using the Kubo formalism. This analysis provides a
quantitative fit to the experimental data over a wide range of carrier
densities. It demonstrates the predominance of carrier scattering by low energy
transverse acoustic (TA) mode phonons: the magnetophonon resonance amplitude is
significantly stronger for the TA modes than for the longitudinal acoustic (LA)
modes. We demonstrate that the LA and TA phonon speeds and the electron-phonon
coupling strengths determined from the magnetophonon resonance measurements
also provide an excellent fit to the measured dependence of the resistivity at
zero magnetic field over a temperature range of 4-150 K. A semiclassical
description of magnetophonon resonance in graphene is shown to provide a simple
physical explanation for the dependence of the magneto-oscillation period on
carrier density. The correspondence between the quantum calculation and the
semiclassical model is discussed.
