Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras

We give various necessary and sufficient conditions for an AF-algebra to be isomorphic to a graph C^*-algebra, an Exel-Laca algebra, and an ultragraph C^*-algebra. We also explore consequences of these results. In particular, we show that all stable AF-algebras are both graph C^*-algebras and Exel-Laca algebras, and that all simple AF-algebras are either graph C^*-algebras or Exel-Laca algebras. In addition, we obtain a characterization of AF-algebras that are isomorphic to the C^*-algebra of a row-finite graph with no sinks.