I have to agree that investing in early stage technology is usually profitless. The pattern is that early investors lose money and eventually sell to someone else at a knock down price. The "someone else" makes a fortune.
One company that in a very small way is graphene related is:
Imperial InnovationsAnother company that commercialises university research (not apparently graphene) is:
Fusion IPDurham Graphene Sciencehas some funding from:
IP Group PLCI found the Durham link here:
Understanding Nano dot ComYou can follow up the other links yourself :-)
I knew about Imperial Innovations, looked it up in Sharescope (which you have to buy), saw that it was categorised as Specialty Finance, ran my eye down the rest of the category and recognised a few more names. You could try Digitallook.com which is free, or the London Stock Exchange site which has quite comprehensive company information.
Then I used Google with searches on e.g. who makes graphene
Let us know if you manage to make any money!