Automorphism groups of wreath product digraphs

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Dobson, Edward
Morris, Joy
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Electronic Journal of Combinatorics
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).
Sherpa Romeo green journal: open access
Color graphs , Graphs , Automorphism , Wreath product
Dobson, E., & Morris, J. (2009). Automorphism groups of wreath product digraphs. Electronic Journal of Combinatorics, 16(1), R17