For a row-finite graph G with no sinks and in which every loop has an exit, we construct an isomorphism between Ext (C~*(G)) and coker (A-I), where A is the vertex matrix of G. If c is the class in Ext (C~* (G)) associated to a graph obtained by attaching a sink to G, then this isomorphism maps c to the class of a vector that describes how the sink was added. We conclude with an application in which we use this isomorphism to produce an example of a row-finite transitive graph with no sinks whose associated C~*-algebra is not semiprojective.
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