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

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