Highly regular vertex-transitive graphs are globally rigid
Combinatorics
2026-01-19 v1
Abstract
A graph is said to be globally rigid in -dimensional space if almost all of its embeddings are unique up to isometries. If a graph has enough automorphisms to send any of its vertices into any other, then it is called vertex-transitive. We show that, in any dimension, highly regular vertex-transitive graphs are globally rigid, positively answering a conjecture of Sean Dewar. Furthermore, we construct examples that show that our constant for regularity is best possible.
Cite
@article{arxiv.2601.11240,
title = {Highly regular vertex-transitive graphs are globally rigid},
author = {Angelo El Saliby},
journal= {arXiv preprint arXiv:2601.11240},
year = {2026}
}