  We study generalized spin waves in graphene under a strong magnetic field
when the Landau-level filling factor is $\nu=\pm 1$. In this case, the ground
state is a particular SU(4) quantum Hall ferromagnet, in which not only the
physical spin is fully polarized but also the pseudo-spin associated with the
valley degree of freedom. The nature of the ground state and the spin-valley
polarization depend on explicit symmetry breaking terms that are also reflected
in the generalised spin-wave spectrum. In addition to pure spin waves, one
encounters valley-pseudo-spin waves as well as more exotic entanglement waves
that have a mixed spin-valley character. Most saliently, the SU(4)
symmetry-breaking terms do not only yield gaps in the spectra, but under
certain circumstances, namely in the case of residual ground-state symmetries,
render the originally quadratic (in the wave vector) spin-wave dispersion
linear.
