Abstract
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 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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The second author is supported in part by the Natural Sciences and Engineering Research Council of Canada.
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Dobson, E., Morris, J. & Spiga, P. Further restrictions on the structure of finite DCI-groups: an addendum. J Algebr Comb 42, 959–969 (2015). https://doi.org/10.1007/s10801-015-0612-3
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DOI: https://doi.org/10.1007/s10801-015-0612-3