  We present the complete formalism that describes scattering in graphene at
low-energies. We begin by analyzing the real-space free Green's function
matrix, and its analytical expansions at low-energy, carefully incorporating
the discrete lattice structure, and arbitrary forms of the atomic-orbital wave
function. We then compute the real-space Green's function in the presence of an
impurity. We express our results both in 2X2 and 4X4 forms (for the two
sublattices and the two inequivalent valleys of the first Brillouin zone). We
compare this with the 4X4 formalism proposed in cond-mat/0608228 and
cond-mat/0702019, and show that the latter is incomplete. We describe how it
can be adapted to accurately take into account the effects of inter-valley
scattering on spatially-varying quantities such as the local density of states.
