Trivalent vertex-transitive graphs with infinite vertex-stabilizers
Combinatorics
2021-01-12 v1 Group Theory
Abstract
We study groups acting vertex-transitively on connected, trivalent graphs such that stabilizers of vertices are infinite. If the action is edge-transitive, we prove that the graph has to be a tree. We analyze the case where the action is not edge-transitive and fully classify the possible -ended graphs. We draw connections to Willis' scale function and re-prove a result by Trofimov.
Cite
@article{arxiv.2101.04064,
title = {Trivalent vertex-transitive graphs with infinite vertex-stabilizers},
author = {Arnbjörg Soffía Árnadóttir and Waltraud Lederle and Rögnvaldur G. Möller},
journal= {arXiv preprint arXiv:2101.04064},
year = {2021}
}