Why are the melting and boiling points of graphite, and diamond so high?
Because both graphite and diamond are non-molecular species, in which each constituent C atom is bound to other carbon atoms by strong chemical bonds.
Both diamond and graphite are network covalent materials. There are no discrete molecules, and vaporization would mean disrupting strong interatomic (covalent) bonds. I am not sure of the physical properties of buckminsterfullerene, 60 carbon atoms arranged in a football shape, but because this species is molecular, its melting/boiling points would be substantially lower than its non-molecular analogues. So, because we are physical scientists, this is your homework: find the melting points of the three carbon allotropes and rationalize them on the basis of their molecularity.
Both have a similar reason as their structure is very similar; the difference is graphite has layers "connected' by weak inter-molecular forces.
A lot of energy is needed to overcome the strong covalent bonds between the carbon atoms. Thus, it has high melting and boiling points.
Though little energy is needed to overcome the weak inter-molecular forces between the layers, a lot of energy is still needed to overcome the strong covalent bonds between the carbon atoms.