The topological dimension of limits of graph substitutions
نویسندگان
چکیده
In 1998, J. Previte developed a framework for studying the dynamics of iterated replacements of certain vertices in a finite graph G by a finite graph H (see [3]). He showed that, except for special cases, the sequence of graphs formed by iterating vertex replacements converges in the Gromov-Hausdor¤ metric. In this paper we prove that the topological dimension of these limit spaces is one. We also provide examples of graph substitutions whose limit spaces are fractals. 1991 Mathematics Subject Classification: 05C10; 37B99.
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