Geodesic
On finite self-complementary metacirculants
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 1135-1144.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove that the automorphism group of a self-complementary metacirculant is either soluble or has $\mathrm A_5$ as the only insoluble composition factor, extending a result of C. H. Li and C. E. Praeger [J. Algebra 349, No. 1, 117--127 (2012; Zbl 1257.20002)] which says the automorphism group of a self-complementary circulant is soluble. The proof involves a construction of self-complementary metacirculants which are Cayley graphs and have insoluble automorphism groups. To the best of our knowledge, these are the first examples of self-complementary graphs with this property.
Classification : 05C25, 20B05, 20B10
Keywords: self-complementary, vertex-transitive, metacirculants 
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Li, Cai Heng; Rao, Guang; Song, Shu Jiao. On finite self-complementary metacirculants. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 1135-1144. http://geodesic.mathdoc.fr/item/JAC_2014__40_4_a0/