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arXiv · 1301.0393

Distinguishing graphs with intermediate growth

Florian Lehner
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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 finite graph with infinite motion and growth at most O(2^((1-\varepsilon) \sqrt(n)/2)) 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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Florian Lehner. 2013-01-08. Distinguishing graphs with intermediate growth. https://arxiv.org/abs/1301.0393

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