Study of quantum symmetries for vertex-transitive graphs using intertwiner spaces

Chassaniol, Arthur

doi:10.48550/arxiv.1904.00455

Cited by 3 publications

(7 citation statements)

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“…It was already shown in [2] that the Paley graph P 9 has no quantum symmetry and in [9] that P 13 and P 17 have no quantum symmetry. We give alternative proofs of these facts in Subsection 4.5.…”

Section: Name Of γmentioning

confidence: 98%

“…Note that it was already shown in [2] that P 9 has no quantum symmetry. In [9], it was proven that P 13 and P 17 have no quantum symmetry. Thus, we just give alternative proofs of those facts.…”

Section: 4mentioning

confidence: 99%

“…In [2], Banica and Bichon computed the quantum automorphism groups of vertex transitive graphs up to order eleven, except the Petersen graph. There are also results for the quantum automorphism groups of circulant graphs, see [9,3].…”

Section: Introductionmentioning

confidence: 99%

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On the quantum symmetry of distance-transitive graphs

Schmidt

2020

Advances in Mathematics

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In this article, we study quantum automorphism groups of distancetransitive graphs. We show that the odd graphs, the Hamming graphs H(n, 3), the Johnson graphs J(n, 2) and the Kneser graphs K(n, 2) do not have quantum symmetry. We also give a table with the quantum automorphism groups of all cubic distance-transitive graphs. Furthermore, with one graph missing, we can now decide whether or not a distance-regular graph of order ≤ 20 has quantum symmetry. Moreover, we prove that the Hoffman-Singleton graph has no quantum symmetry. On a final note, we present an example of a pair of graphs with the same intersection array (the Shrikhande graph and the 4 × 4 rook's graph), where one of them has quantum symmetry and the other one does not. The author is supported by the DFG project Quantenautomorphismen von Graphen. He thanks his supervisor Moritz Weber for proofreading the article and many helpful comments and suggestions. This article is part of the author's PhD thesis.Theorem 1.4. For n ≥ 5, the Johnson graphs J(n, 2) and the Kneser graphs K(n, 2) do not have quantum symmetry.

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Section: Name Of γmentioning

confidence: 98%

Section: 4mentioning

confidence: 99%

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On the quantum symmetry of distance-transitive graphs

Schmidt

2020

Advances in Mathematics

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“…The equivalence of the two generating sets can be easily seen by noticing that ) on the other hand. See also [Cha19].…”

Section: Definition 22 ([Ban05]mentioning

confidence: 99%

“…As a side remark, let us mention the work of Chassaniol [Cha19], who uses the intertwiner approach to determine quantum symmetries of some circulant graphs, i.e. Cayley graphs of the cyclic groups.…”

Section: Introductionmentioning

confidence: 99%