A finite group R is a DCI-group if, whenever S and T are subsets of R with the Cayley digraphs Cay(R,S) and Cay(R,T) isomorphic, there exists an automorphism φ of R with Sφ=T. The classification of 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≥5 prime, is a DCI-group. This corrects and completes the proof of Li et al. (J Algebr Comb 26:161–181, 2007, Theorem 1.1) as observed by the reviewer (Conder in Math review MR2335710).
Dobson, E., Morris, J., Spiga, P. (2015). Further restrictions on the structure of finite DCI-groups: an addendum. JOURNAL OF ALGEBRAIC COMBINATORICS, 42(4), 959-969 [10.1007/s10801-015-0612-3].
Further restrictions on the structure of finite DCI-groups: an addendum
SPIGA, PABLOUltimo
2015
Abstract
A finite group R is a DCI-group if, whenever S and T are subsets of R with the Cayley digraphs Cay(R,S) and Cay(R,T) isomorphic, there exists an automorphism φ of R with Sφ=T. The classification of 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≥5 prime, is a DCI-group. This corrects and completes the proof of Li et al. (J Algebr Comb 26:161–181, 2007, Theorem 1.1) as observed by the reviewer (Conder in Math review MR2335710).
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