Péter P. Pálfy: The isomorphism problem of directed Cayley graphs. Hommage à Rédei

A finite group G is called a DCI-group, if two directed Cayley graphs Cay(G,S) and Cay(G,T) are isomorphic iff there is an automorphism of G that maps S to T. This concept was introduced by László Babai in 1977, motivated by a problem of András Ádám. There is an extensive literature on DCI- and CI-groups (in the latter case one considers only undirected Cayley graphs). A recent progress makes it possible to reduce the problem of determining DCI-groups to three easily formulated particular cases. I will present a sketch of proof that utilizes a counting argument almost the same as in Rédei's 1950 paper in Acta Mathematica.
 

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