The graded Grothendieck group and the classication of Leavitt path algebras

This paper is an attempt to show that, parallel to Elliott's classification of AF C*-algebras by means of K-theory, the graded K 0-group classifies Leavitt path algebras completely. In this direction, we prove this claim at two extremes, namely, for the class of acyclic graphs (graphs with no cycles) and multi-headed comets or rose graphs (graphs in which each head is connected to a cycle or to a collection of loops), or a mixture of these graphs (i.e., polycephaly graphs).