We consider circulant graphs having vertices, with prime. To any such graph we associate a certain number , that we call type of the graph. We prove that for the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.
On considère des graphes circulants ayant sommets, avec premier. A un tel graphe on associe un certain nombre , qu’on appelle type du graphe. On montre que pour le graphe n’a pas de symétrie quantique, dans le sens où son groupe quantique d’automorphismes est réduit à son groupe classique d’automorphismes.
Keywords: Quantum permutation group, circulant graph
Mot clés : groupe quantique de permutation, graphe circulant
Banica, Teodor 1; Bichon, Julien 2; Chenevier, Gaëtan 3
@article{AIF_2007__57_3_955_0, author = {Banica, Teodor and Bichon, Julien and Chenevier, Ga\"etan}, title = {Graphs having no quantum symmetry}, journal = {Annales de l'Institut Fourier}, pages = {955--971}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {57}, number = {3}, year = {2007}, doi = {10.5802/aif.2282}, zbl = {1178.05047}, mrnumber = {2336835}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2282/} }
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 SP - 955 EP - 971 VL - 57 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2282/ DO - 10.5802/aif.2282 LA - en ID - AIF_2007__57_3_955_0 ER -
%0 Journal Article %A Banica, Teodor %A Bichon, Julien %A Chenevier, Gaëtan %T Graphs having no quantum symmetry %J Annales de l'Institut Fourier %D 2007 %P 955-971 %V 57 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2282/ %R 10.5802/aif.2282 %G en %F AIF_2007__57_3_955_0
Banica, Teodor; Bichon, Julien; Chenevier, Gaëtan. Graphs having no quantum symmetry. Annales de l'Institut Fourier, Volume 57 (2007) no. 3, pp. 955-971. doi : 10.5802/aif.2282. https://aif.centre-mersenne.org/articles/10.5802/aif.2282/
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