It is a priori a difficult problem to find, given an abelian semigroup M (with, say, some presentation in terms of generators and relations), a C*-algebra A whose semigroup of Murray von Neumann equivalence classes of projections V (A) is isomorphic to M. In this talk I will discuss conditions on M that allow such a representation result to hold, in the form of a graph C*-algebra. This is joint work with Pere Ara (Barcelona) and Friedrich Wehrung (Caen).