All of carbon atoms in diamond, graphite and graphene are linked together by strong covalent bonds
Diamond and graphite exist as giant covalent structures
In diamond, each carbon atom is covalently bonded to four other carbon atoms in a giant repeating pattern
Each covalent bond is strong and difficult to break and this makes diamond very hard
As diamond has strong covalent in a giant structure it has very high melting and boiling points
There are no charged particles in diamond or any free electrons to carry an electric current so it doesn't conduct in the liquid or solid state
In graphite, the carbon atoms are in layers of hexagonal rings where each carbon atom is covalently bonded to three other carbon. This means that each carbon has a spare electron which is free to move through the layers so graphite conducts electricity both as a solid and as a liquid
The covalent bonds in layers are strong but between the layers there are only weak inter molecular forces. These are easy to break and so the layers can slide over each other easily, making graphite very soft and slippery. This means it can be used in industry as a lubricant
Graphite also have high melting and boiling points because to melt graphite all of its strong covalent bonds have to be broken and this requires lots of energy
Graphene has an identical structure to a single layer of graphite. This means that it is one atom thick
It also means that graphene has identical properties to one layer of graphite, making it strong, flexible, transparent and s good electrical conductor. These properties give it lots of potential uses in, for example, electrical circuits