  Statistical distribution of energy levels for Dirac fermions confined in a
quantum dot is studied numerically on the examples of triangular and hexagonal
graphene flakes with random electrostatic potential landscape. When increasing
the disorder strength, level distribution evolves from Poissonian to Wigner,
indicating the transition to quantum chaos. The unitary ensemble (with the
twofold valley degeneracy) is observed for triangular flakes with zigzag or
Klein edges and potential varying smoothly on the scale of atomic separation.
For small number of edge defects, the unitary-to-orthogonal symmetry transition
is found at zero magnetic field. For remaining systems, the orthogonal ensemble
appears. These findings are rationalized by means of additive random-matrix
models for the cases of weak and strong intervalley scattering of charge
carriers in graphene. The influence of weak magnetic fields, as well as the
strong-disorder-induced wavefunction localization, on the level distribution is
also briefly discussed.
