Geodesic
Further restrictions on the structure of finite DCI-groups: an addendum
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 959-969.

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

A finite group $R$ is a ${\mathrm {DCI}}$-group if, whenever $S$ and $T$ are subsets of $R$ with the Cayley digraphs ${\mathrm {Cay}}(R, S)$ and ${\mathrm {Cay}}(R, T)$ isomorphic, there exists an automorphism $\varphi$ of $R$ with $S^\varphi = T$. The classification of ${\mathrm {DCI}}$-groups is an open problem in the theory of Cayley digraphs and is closely related to the isomorphism problem for digraphs. This paper is a contribution toward this classification, as we show that every dihedral group of order $6p$, with $p\ge 5$ prime, is a ${\mathrm {DCI}}$-group. This corrects and completes the proof of C. H. Li et al. [J. Algebr. Comb. 26, No. 2, 161--181 (2007; Zbl 1124.05045), Theorem 1.1] as observed by the reviewer (Conder in Mathematical Reviews MR2335710).
Classification : 05C25, 05C60, 05C20
Keywords: Cayley graph, isomorphism problem, CI-group, dihedral group 
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Dobson, Edward; Morris, Joy; Spiga, Pablo. Further restrictions on the structure of finite DCI-groups: an addendum. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 959-969. http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a8/