  In this paper we give a complete description of K-theory groups for
Cuntz-Krieger C*-algebras associated to general locally-finite (topologically
connected) graphs via Bass-Hashimoto operator. Our result generalizes the one
obtained by the second author for the case of graphs with not necessarily
finite first Betti numbers. On the basis of purely graph-theoretical method
introduced by G. Cornelissen, O. Lorscheid, M. Marcolli and developed further
by N.Iyudu, we prove that for the algebra O_E associated to an infinite graph E
of the above form holds K_0(O_E)=Z^{\beta(E)} \oplus Z^{\gamma(E)} and K_1(O_E)
= Z^{\gamma(E)}, where \beta(E)=\dim H_1(E) and \gamma(E) stands for the
cardinality of the valency set of E, defined in the paper.

Operator Algebras;K-Theory and Homology;Rings and Algebras