Distinguishing graphs with intermediate growth |
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Authors: | Florian Lehner |
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Affiliation: | 1.Department of Mathematics,Universit?t Hamburg,Hamburg,Germany |
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Abstract: | A graph G is said to be 2-distinguishable if there is a 2-labeling of its vertices which is not preserved by any nontrivial automorphism of G. We show that every locally finte graph with infinite nite motion and growth at most (mathcal{O}left( {2^{(1 - varepsilon )tfrac{{sqrt n }}{2}} } right)) is 2-distinguishable. Infinite motion means that every automorphism moves infinitely many vertices and growth refers to the cardinality of balls of radius n. |
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