Stability of C*-algebras associated to graphs

We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C* (G) is stable if and only if each vertex in G can be reached by an infinite number of vertices. We use this characterization to realize the stabilization of a graph C*-algebra. Specifically, if G is a graph and (G) over tilde is the graph formed by adding a head to each vertex of G, then C*((G) over tilde) is the stabilization of C* ((G) over tilde); that is, C* (0) congruent to C* (G) circle times K.