  When the phonon spectrum of a material is measured in a scattering
experiment, selection rules preclude the observation of phonons that are odd
under reflection by the scattering plane. Understanding these rules is crucial
to correctly interpret experiments and to detect broken symmetries. Taking
graphene as a case study, in this work we derive the complete set of selection
rules for the honeycomb lattice, showing that some of them have been missed or
misinterpreted in the literature. Focusing on the technique of high-resolution
electron energy loss spectroscopy (HREELS), we calculate the scattering
intensity for a simple force constant model to illustrate these rules. In
addition, we present HREELS measurements of the phonon dispersion for graphene
on Ru(0001) and find excellent agreement with the theory. We also illustrate
the effect of different symmetry breaking scenarios in the selection rules and
discuss previous experiments in light of our results.
