Limits of vertex replacement rules

Joseph Previte, Michelle Previte, Mary Vanderschoot

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In an earlier paper [10], J. Previte developed a framework for studying iterated replacements of certain vertices in a graph G by a finite replacement graph H. He showed that the normalized sequence of iterated graphs converges in the Gromov-Hausdorff metric (except for special cases). In this paper, we extend the framework in [10] to iterated vertex replacements where there are at least two replacement graphs and prove a convergence result. We also give examples of vertex replacement rules that yield convergent sequences of graphs.

Original languageEnglish (US)
Pages (from-to)1001-1026
Number of pages26
JournalRocky Mountain Journal of Mathematics
Volume37
Issue number3
DOIs
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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