Distinguishing graphs with intermediate growth
Combinatorics
2013-01-09 v2
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.
Keywords
Cite
@article{arxiv.1301.0393,
title = {Distinguishing graphs with intermediate growth},
author = {Florian Lehner},
journal= {arXiv preprint arXiv:1301.0393},
year = {2013}
}