Graphene is a single layer of graphite. The strong covalent bonds between the carbon atoms mean that graphene:
Fullerenes are molecules of carbon atoms with hollow shapes. Their structures are based on hexagonal rings of carbon atoms joined by covalent bonds. Some fullerenes include rings with five or seven carbon atoms. Two examples of fullerenes are buckminsterfullerene and nanotubes.
Buckminsterfullerene was the first fullerene to be discovered. Its molecules are made up of 60 carbon atoms joined together by strong covalent bonds. Molecules of C60 are spherical.
There are weak intermolecular forces between molecules of buckminsterfullerene. These need little energy to overcome, so buckminsterfullerene is slippery and has a low melting point.
A nanotube is like a layer of graphene, rolled into a cylinder. The length of a nanotube is very long compared to its width, so nanotubes have high length to diameter ratios.
These properties make nanotubes useful for nanotechnology, electronics and specialised materials.