2015
DOI: 10.1007/s10801-015-0612-3
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Further restrictions on the structure of finite DCI-groups: an addendum

Abstract: A finite group R is a DCI-group if, whenever S and T are subsets of R with the Cayley graphs Cay(R, S) and Cay(R, T ) isomorphic, there exists an automorphism ϕ of R with S ϕ = T .The classification of DCI-groups is an open problem in the theory of Cayley graphs and is closely related to the isomorphism problem for graphs. This paper is a contribution towards 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 [5, The… Show more

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Cited by 13 publications
(17 citation statements)
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“…We believe that every generalised dihedral group satisfying this numerical condition on its order is a genuine CI-group. (This is in line with the partial result in [8].) Additionally, this result further reduces to two other groups on the list, whose definitions we now give.…”
Section: Introductionsupporting
confidence: 85%
See 1 more Smart Citation
“…We believe that every generalised dihedral group satisfying this numerical condition on its order is a genuine CI-group. (This is in line with the partial result in [8].) Additionally, this result further reduces to two other groups on the list, whose definitions we now give.…”
Section: Introductionsupporting
confidence: 85%
“…The first author [4,Theorem 22] extended this to some special values of square-free integers. With Joy Morris, the first and third authors [8] showed that D 6p is a CI-group, p ≥ 5. Also, Li, Lu, and Pálfy showed E(p, 4) and E(p, 8) are CI-groups.…”
Section: Introductionmentioning
confidence: 99%
“…The next result is a combination of results of Li, Lu, and Pálfy [9], and Somlai [11], and lists all possible CI-groups with respect to graphs. Not every group in this result is known to be a CI-group with respect to graphs -see [6] for a recent list of the known CI-groups with respect to graphs.…”
Section: Definitionmentioning
confidence: 99%
“…Motivated by a problem posed by Ádám in [1], Babai and Frankl [4] asked the following question: Which are the CI-groups? Although the candidates of CI-groups have been reduced to a restricted list [9,17], which was obtained by accumulating the work of several mathematicians, it is considered to be difficult to confirm that a particular group is a CI-group. We refer the reader to the survey paper [18] for most results on CI-and DCI-groups.…”
Section: Introductionmentioning
confidence: 99%