  The electronic shell and supershell structure of triangular graphene quantum
dots has been studied using density functional and tight-binding methods. The
density functional calculations demonstrate that the electronic structure close
to the Fermi energy is correctly described with a simple tight-binding model
where only the p_z orbitals perpendicular to the graphene layer are included.
The results show that (i) both at the bottom and at the top of the p_z band a
supershell structure similar to that of free electrons confined in a triangular
cavity is seen, (ii) close to the Fermi level the shell structure is that of
free massless particles, (iii) triangles with armchair edges show an additional
sequence of levels ('ghost states') absent for triangles with zigzag edges
while the latter exhibit edge states, and (iv) the observed shell structure is
rather insensitive to the edge roughness.
