Das, M.; Edgar, G. A. Finite type, open set conditions and weak separation conditions. (English) Zbl 1226.28004 Nonlinearity 24, No. 9, 2489-2503 (2011). Summary: We study graph-directed iterated function systems of finite type. We show that such an IFS of finite type induces another graph-directed IFS of finite type where every strongly connected component satisfies the open set condition. We introduce the notions of topological and geometric weak separation properties, and summarize the relationship between the different separation conditions. For the induced IFS, similarity, growth, box and Hausdorff dimension coincide. Finally, we prove that the generalized finite-type condition for graphs implies the geometric weak separation property. Cited in 3 Documents MSC: 28A78 Hausdorff and packing measures 28A80 Fractals 05C10 Planar graphs; geometric and topological aspects of graph theory Keywords:graph-directed IFS; graph finite-type condition PDFBibTeX XMLCite \textit{M. Das} and \textit{G. A. Edgar}, Nonlinearity 24, No. 9, 2489--2503 (2011; Zbl 1226.28004) Full Text: DOI