  A quantum graph model for a single sheet of graphene is extended to bilayer
and trilayer Bernal-stacked graphene; the spectra are characterized and the
dispersion relations explicitly obtained; Dirac cones are then proven to be
present only for trilayer graphene, although the bilayer has a gapless
parabolic band component. Our model rigorously exhibits basic facts from
tight-binding calculations, effective two-dimensional models and a
$\pi$-orbital continuum model with nearest-neighbour tunneling that have been
discussed in the physics literature.
