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Combinatorica

, Volume 36, Issue 3, pp 333–347 | Cite as

Distinguishing graphs with intermediate growth

  • Florian LehnerEmail author
Original Paper

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.

Mathematics Subject Classification

05C25 05C15 20B27 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversität HamburgHamburgGermany

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