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 ). 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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics