  Graphene nanodisk is a graphene derivative with a closed edge. The trigonal
zigzag nanodisk with size $N$ has $N$-fold degenerated zero-energy states. We
investigate electron-electron interaction effects in the zero-energy sector. We
explicitely derive the direct and exchange interactions, which are found to
have no SU($N$) symmetry. Then, regarding a nanodisk as a quantum dot with an
internal degree of freedom, we analyze the nanodisk-lead system consisting of a
nanodisk and two leads. Employing the standard Green function method, we reveal
novel Coulomb blockade effects in the system. The occupation number in the
nanodisk exhibits a peculiar series of plateaux and dips, reflecting a peculiar
structure of energy spectrum of nanodisk without SU($N$) symmetry. Dips are
argued to emerge due to a Coulomb correlation effect.
