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.

8 pages, 5 figures