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PreprintarXiv licencearXiv

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 M2(ℂ) are vertex-transitive, but many simple quantum graphs in M3(ℂ) are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in M3(ℂ) up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in Mn(ℂ), which we call the panoramic polynomial.

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Cite

BibTeXRIS
BibTeX
@misc{hayes2026vertextransitive,
  title = {{Vertex-transitive quantum graphs}},
  author = {Mac Hayes and Trevor Jess and Andre Kornell and Remi Salinas Schmeis},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.30730},
  eprint = {2605.30730},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.30730},
}
RIS
TY  - UNPB
TI  - Vertex-transitive quantum graphs
AU  - Mac Hayes
AU  - Trevor Jess
AU  - Andre Kornell
AU  - Remi Salinas Schmeis
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2605.30730
UR  - https://arxiv.org/abs/2605.30730
AB  - 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(ℂ) are vertex-transitive, but many simple quantum graphs in M_3(ℂ) are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in M_3(ℂ) up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in M_n(ℂ), which we call the panoramic polynomial.
ER  -