The topological dimension of limits of vertex replacements

Michelle Previte, Shun Hsiang Yang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Given an initial graph G, one may apply a rule R to G which replaces certain vertices of G with other graphs called replacement graphs to obtain a new graph R ( G ). By iterating this procedure, a sequence of graphs { Rn ( G ) } is obtained. When each graph in this sequence is normalized to have diameter one, the resulting sequence may converge in the Gromov-Hausdorff metric. In this paper, we compute the topological dimension of limit spaces of normalized sequences of iterated vertex replacements involving more than one replacement graph. We also give examples of vertex replacement rules that yield fractals.

Original languageEnglish (US)
Pages (from-to)2013-2025
Number of pages13
JournalTopology and its Applications
Volume153
Issue number12
DOIs
StatePublished - Jun 1 2006

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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