Geodesic
On dihedrants admitting arc-regular group actions
Journal of Algebraic Combinatorics, Tome 33 (2011) no. 3, pp. 409-426.

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

Summary: We consider Cayley graphs $\Gamma $ over dihedral groups, $dihedrants$ for short, which admit an automorphism group $G$ acting regularly on the arc set of $\Gamma $. We prove that, if $D _{2 n }\leq G\leq Aut( \Gamma )$ is a regular dihedral subgroup of $G$ of order $2 n$ such that any of its index 2 cyclic subgroups is core-free in $G$, then $\Gamma $ belongs to the family of graphs of the form $( K _{ n $_1 Ä frac14 Ä $K _{ n $_ l$)[ K _{ m} ^{ c}]$ (K_n_1otimescdots$\otimes $K_n_ell)[K_m^mathrmc], where $2 n= n _{1}\cdot \cdot \cdot n _{ \ell } m$, and the numbers $n _{ i }$ are pairwise coprime. Applications to 1-regular dihedrants and Cayley maps on dihedral groups are also given.
Classification : transitive, circulants,, see, [18,, Theorem, 3
Keywords: keywords arc-transitive graph, Cayley graph, Cayley map, dihedral group, core-free group 
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     title = {On dihedrants admitting arc-regular group actions},
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     pages = {409--426},
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Kovács, István; Marušič, Dragan; Muzychuk, Mikhail E. On dihedrants admitting arc-regular group actions. Journal of Algebraic Combinatorics, Tome 33 (2011) no. 3, pp. 409-426. http://geodesic.mathdoc.fr/item/JAC_2011__33_3_a3/