A unital graph C*-algebra is operator norm stable exactly when a certain reachability subgraph is finite, and is residually finite-dimensional exactly when the graph is finite and no cycle has an entry.
Dadarlat, Nonnuclear Subalgebras of AF Algebras, American Journal of Mathematics 122(3): 581–597, 2000
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Decomposition theorems for unital graph C*-algebras
A unital graph C*-algebra is operator norm stable exactly when a certain reachability subgraph is finite, and is residually finite-dimensional exactly when the graph is finite and no cycle has an entry.