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For a row finite directed graph E, Kumjian, Pask, and Raeburn proved that there exists a universal C * -algebra C * (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density problems of invertible elements in graph C * -algebras C * (E), and it is proved that C * (E) has stable rank one, that is, the set of all invertible elements is dense in C * (E) (or in its unitization when C * (E) is nonunital) if and only if no loop of E has an exit. We also prove that for a locallydoi:10.2140/pjm.2001.200.331 fatcat:lxmggjtk7jbfhn43rv7o6kjwtu