Vertex-transitive quantum graphs

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.

Operator Algebras (math.OA); Combinatorics (math.CO); Quantum Algebra (math.QA); Quantum Physics (quant-ph)

arXiv:2605.30730 [math.OA]

(or arXiv:2605.30730v2 [math.OA] for this version)

https://doi.org/10.48550/arXiv.2605.30730 Focus to learn more arXiv-issued DOI via DataCite

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