The Growth of Limits of Vertex Replacement Rules |
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| Authors: | Joseph Previte Michelle Previte Mary Vanderschoot |
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| Affiliation: | 1. DEPARTMENT OF MATHEMATICS, PENN STATE ERIE, THE BEHREND COLLEGE, , PENNSYLVANIA;2. DEPARTMENT OF MATHEMATICS, WHEATON COLLEGE, , WHEATON, ILLINOIS |
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| Abstract: | In this article, we give conditions to distinguish whether a vertex replacement rule given by a single graph H yields a limit graph having polynomial or exponential growth. In the case of polynomial growth, we compute the growth degree of the limit graph. |
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| Keywords: | growth degree Hausdorff dimension vertex replacement rules graph substitutions |
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