The topological dimension of limits of graph substitutions

Michelle Previte, Mary Vanderschoot

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

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-Hausdorff 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.

Original languageEnglish (US)
Pages (from-to)477-487
Number of pages11
JournalForum Mathematicum
Volume15
Issue number3
DOIs
StatePublished - Jan 1 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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