Geodesic
On $G$-arc-regular dihedrants and regular dihedral maps
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 437-455.

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

Summary: A graph $\Gamma $ is said to be G-arc-regular if a subgroup $G \le\operatorname{\mathsf{Aut}}(\varGamma)$ acts regularly on the arcs of $\Gamma $. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D $_{2n }$ of order 2n whose cyclic subgroup C $_{ n }\leq D _{2n }$ of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D $_{2n }$, n odd, are classified.
Keywords: G-arc-regular graph, Cayley graph, Cayley map, dihedral group 
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     title = {On $G$-arc-regular dihedrants and regular dihedral maps},
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Kovács, István; Marušič, Dragan; Muzychuk, Mikhail. On $G$-arc-regular dihedrants and regular dihedral maps. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 437-455. http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a2/