  Experiments on hexagonal graphene-like structures using microwave measuring
techniques are presented. The lowest transverse-electric resonance of coupled
dielectric disks sandwiched between two metallic plates establishes a
tight-binding configuration. The nearest-neighbor coupling approximation is
investigated in systems with few disks. Taking advantage of the high
flexibility of the disks positions, consequences of the disorder introduced in
the graphene lattice on the Dirac points are investigated. Using two different
types of disks, a boron-nitride-like structure (a hexagonal lattice with a
two-atom basis) is implemented, showing the appearance of a band gap.
