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arXiv · 2601.11240

Highly regular vertex-transitive graphs are globally rigid

Angelo El Saliby
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Abstract

A graph is said to be globally rigid in $d$-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.

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Angelo El Saliby. 2026-01-16. Highly regular vertex-transitive graphs are globally rigid. https://arxiv.org/abs/2601.11240

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