Towards a K-theoretic characterization of graded isomorphisms between   Leavitt path algebras
  Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs. 
P. Ara, E. Pardo
math.RA math.OA