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arXiv · 2605.30730

Vertex-transitive quantum graphs

Mac Hayes·Trevor Jess·Andre Kornell·Remi Salinas Schmeis
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Abstract

We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classical case. All simple quantum graphs in $M_2(\mathbb C)$ are vertex-transitive, but many simple quantum graphs in $M_3(\mathbb C)$ are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in $M_3(\mathbb C)$ up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in $M_n(\mathbb C)$, which we call the panoramic polynomial.

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BibTeXRIS

Mac Hayes, Trevor Jess, Andre Kornell, Remi Salinas Schmeis. 2026-05-29. Vertex-transitive quantum graphs. https://arxiv.org/abs/2605.30730

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