Vertex-transitive quantum graphs

• URL: http://arxiv.org/abs/2605.30730v2
• Date: Mon, 01 Jun 2026 22:36:22 GMT
• Title: Vertex-transitive quantum graphs
• Abstract summary: We provide a complete classification of quantum graphs in $M_3(mathbb C)$ up to isomorphism.<n>To do this, we introduce a invariant for quantum graphs in $M_n(mathbb C)$, which we call the panoramic.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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