Geodesic
On the Minimum Order of Graphs with Given Group
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 467-470

Voir la notice de l'article provenant de la source Cambridge University Press

For G a, finite group let α(G) denote the minimum number of vertices of the graphs X the automorphism group A(X) of which is isomorphic to G.G. Sabidussi proved [1], that α(G)=0(n log d) where n=\G\ and d is the minimum number of generators of G.As 0(log n) is the best possible upper bound for d, the result established in [1] implies that α(G)=0(n log log n). 
Babai, László. On the Minimum Order of Graphs with Given Group. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 467-470. doi: 10.4153/CMB-1974-082-9
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[1] 1. Sabidussi, G., On the minimum order of graphs with given automorphism group, Monatsh. Math. 63, (1959) pp. 124-127. Google Scholar

[2] 2. Harary, F. and Palmer, E., The smallest graph whose group is cyclic, Czechoslovak Math. J. 16,(91)(1966), pp. 70-71. Google Scholar

[3] 3. Sabidussi, G., Review 2563, Math. Rev. 33, No. 3, March 1967. 1500 Google Scholar

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