  In the last few years, the fascinating properties of graphene have been
thoroughly investigated. The existence of Dirac cones is the most important
characteristic of the electronic band-structure of graphene. In this
theoretical paper, hexagonal monolayers of silicon (h-Si) and germanium (h-Ge)
are examined using density functional theory, within the generalized gradient
approximation. Our numerical results indicate that both h-Si and h-Ge are
chemically stable. The lattice parameters, electronic dispersion relations and
densities of states for these systems are reported. The electronic dispersion
relations display Dirac cones with the symmetry of an equilateral triangle (the
group D$_3$) in the vicinity of the K points. Hence, the Fermi velocity depends
on the wave vector direction around $K$ points. Fermi velocities for holes and
electrons are significantly different. The maximum and minimum Fermi velocities
are also reported.
