Faithful representations of graph algebras via branching systems
  We continue to investigate branching systems of directed graphs and their connections with graph algebras. We give a sufficient condition under which the representation induced from a branching system of a directed graph is faithful and construct a large class of branching systems that satisfy this condition. We finish the paper by providing a proof of the converse of the Cuntz-Krieger uniqueness theorem for graph algebras by means of branching systems. 
Daniel Gon\c{c}alves, Hui Li and Danilo Royer
math.OA