Graphs having no quantum symmetry

Teodor Banica[1]; Julien Bichon[2]; Gaëtan Chenevier[3]

  • [1] Université Toulouse 3 Département de mathématiques 118, route de Narbonne 31062 Toulouse (France)
  • [2] Université de Pau Département de mathématiques 1, avenue de l’université 64000 Pau (France)
  • [3] Université Paris 13 Département de mathématiques 99, avenue J-B. Clément 93430 Villetaneuse (France)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 3, page 955-971
  • ISSN: 0373-0956

Abstract

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We consider circulant graphs having p vertices, with p prime. To any such graph we associate a certain number k , that we call type of the graph. We prove that for p ≫ k the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

How to cite

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Banica, Teodor, Bichon, Julien, and Chenevier, Gaëtan. "Graphs having no quantum symmetry." Annales de l’institut Fourier 57.3 (2007): 955-971. <http://eudml.org/doc/10247>.

@article{Banica2007,
abstract = {We consider circulant graphs having $p$ vertices, with $p$ prime. To any such graph we associate a certain number $k$, that we call type of the graph. We prove that for $p\gg k$ the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.},
affiliation = {Université Toulouse 3 Département de mathématiques 118, route de Narbonne 31062 Toulouse (France); Université de Pau Département de mathématiques 1, avenue de l’université 64000 Pau (France); Université Paris 13 Département de mathématiques 99, avenue J-B. Clément 93430 Villetaneuse (France)},
author = {Banica, Teodor, Bichon, Julien, Chenevier, Gaëtan},
journal = {Annales de l’institut Fourier},
keywords = {Quantum permutation group; circulant graph; quantum permutation group},
language = {eng},
number = {3},
pages = {955-971},
publisher = {Association des Annales de l’institut Fourier},
title = {Graphs having no quantum symmetry},
url = {http://eudml.org/doc/10247},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Banica, Teodor
AU - Bichon, Julien
AU - Chenevier, Gaëtan
TI - Graphs having no quantum symmetry
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 3
SP - 955
EP - 971
AB - We consider circulant graphs having $p$ vertices, with $p$ prime. To any such graph we associate a certain number $k$, that we call type of the graph. We prove that for $p\gg k$ the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.
LA - eng
KW - Quantum permutation group; circulant graph; quantum permutation group
UR - http://eudml.org/doc/10247
ER -

References

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