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THE HAUSDORFF DIMENSION OF A GRAPH-DIRECTED SET WHOSE UNDERLYING MULTIGRAPH IS A CARTESIAN PRODUCT OR A TENSOR PRODUCT OF MULTIGRAPHS

STEFAAN DELCROIX

Department of Mathematics, California State University, 5245 North Backer Avenue, M/S PB108, Fresno, CA 93740, USA

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and

MICHAEL J. FISHER

Department of Mathematics, West Chester University, West Chester, PA 19383, USA

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https://doi.org/10.1142/S0218348X12500193Cited by:1 (Source: Crossref)

Abstract

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.

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References

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