Morris, Joy

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Automorphism groups of wreath product digraphs
(Electronic Journal of Combinatorics, 2009) Dobson, Edward; Morris, Joy
We generalize a classical result of Sabidussi that was improved by Hemminger, to the case of directed color graphs. The original results give a necessary and suﬃcient condition on two graphs, C and D, for the automorphsim group of the wreath product of the graphs, Aut(C o D) to be the wreath product of the automorphism groups Aut(C) o Aut(D). Their characterization generalizes directly to the case of color graphs, but we show that there are additional exceptional cases in which either C or D is an inﬁnite directed graph. Also, we determine what Aut(C o D) is if Aut(C o D) 6= Aut(C) o Aut(D), and in particular, show that in this case there exist vertex-transitive graphs C0 and D0 such that C0 oD0 = C oD and Aut(C oD) = Aut(C0) o Aut(D0).