Non-stable K-theory for Leavitt path algebras
  We compute the monoid of isomorphism classes of finitely generated projective modules of a Leavitt path algebra over an arbitrary directed graph. Our result generalizes the result of Ara, Moreno, and Pardo in which they computed this monoid of a Leavitt path algebra over a countable row-finite directed graph. 
Damon Hay, Marissa Loving, Martin Montgomery, Efren Ruiz, Katherine   Todd
math.RA