On Regularity of Graph <i>C</i>*-Algebras

We prove that for any countable directed graph E with Condition (K), the corresponding graph C*-algebra C*(E) has nuclear dimension at most two. We also prove that the nuclear dimension of certain extensions is at most one, which can be applied to certain graphs to achieve the optimal upper bound of one. Finally, we generalize some previous results for O∞ -stability of graph algebras, and prove some partial results for Z-stability. Advisor: Christopher Schafhauser