  A $\lambda$-graph system $\frak L$ is a labeled Bratteli diagram with shift
operation. It is a generalized notion of finite labeled graph and presents a
subshifts. We will study continuous orbit equivalence of one-sided subshifts
and topological conjugacy of two-sided subshifts from the view points of
groupoids and $C^*$-algebras constructed from $\lambda$-graph systems.
