The hausdorff dimension of a graph-directed set whose underlying multigraph is a cartesian product or a tensor product of multigraphs

摘要

In this paper, we compute the Hausdorff dimension of a graph-directed set when the underlying multigraph is a Cartesian product or a tensor product of several multigraphs. We give explicit formulas in terms of the eigenvalues of the graph and the similarity ratios used with each graph.