  We study electronic properties of graphene derivatives which have closed
edges. They are finite-length graphene nanoribbons and graphene nanodisks. No
metallic states are found in finite-length zigzag nanoribbons though all
infinite-length zigzag nanoribbons are metallic. We also study hexagonal,
parallelogrammic and trigonal nanodisks with zigzag or armchair edges. No
metallic states are found in these nanodisks either except trigonal zigzag
nanodisks. It is interesting that we can design the degeneracy of the metallic
states arbitrarily in trigonal zigzag nanodisks by changing the size.
