Separation properties for graph-directed self-similar fractals

Examples of “separation properties” for iterated function systems of similitudes include: the open set condition, the weak separation property, finite type. Alternate descriptions for these properties and relations among these properties have been worked out. Here we consider the same situation for “graph-directed” iterated function systems, and provide the definitions and proofs for that setting. We deal with the case of strongly connected graphs. In many cases the definitions (and proofs) are much like the one-node case. But sometimes we have found changes were needed.