  We investigate three formalisms to specify graph languages, i.e. sets of
graphs, based on type graphs. First, we are interested in (pure) type graphs,
where the corresponding language consists of all graphs that can be mapped
homomorphically to a given type graph. In this context, we also study languages
specified by restriction graphs and their relation to type graphs. Second, we
extend this basic approach to a type graph logic and, third, to type graphs
with annotations. We present decidability results and closure properties for
each of the formalisms.
