The topological dimension of limits of vertex replacements

Michelle Previte, Shun Hsiang Yang

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 language English (US) 2013-2025 13 Topology and its Applications 153 12 https://doi.org/10.1016/j.topol.2005.07.008 Published - Jun 1 2006

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Replacement
Graph in graph theory
Vertex of a graph
Hausdorff Metric
Fractal
Converge

All Science Journal Classification (ASJC) codes

• Geometry and Topology

Cite this

Previte, Michelle ; Yang, Shun Hsiang. / The topological dimension of limits of vertex replacements. In: Topology and its Applications. 2006 ; Vol. 153, No. 12. pp. 2013-2025.
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The topological dimension of limits of vertex replacements. / Previte, Michelle; Yang, Shun Hsiang.

In: Topology and its Applications, Vol. 153, No. 12, 01.06.2006, p. 2013-2025.

Research output: Contribution to journalArticle

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