In this paper a K-theoretic classification is given of the C
∗
^*
-algebra dynamical systems
(
A
,
α
,
Z
2
)
=
lim
→
(
A
n
,
α
n
,
Z
2
)
(A, \alpha , Z_2)= \lim \limits _\to (A_n, {\alpha }_n, Z_2)
where
A
A
is of real rank zero, each
A
n
A_n
is a finite direct sum of matrix algebras over finite connected graphs, and each
α
n
\alpha _n
is induced by an action on each component of the spectrum of
A
n
A_n
. Corresponding to the trivial actions is the K-theoretic classification for real rank zero C
∗
^*
-algebras that can be expressed as finite direct sums of matrix algebras over finite graphs obtained in Mem. Amer. Math. Soc. no. 547, vol. 114.