Automorphism Groups of Wreath Product Digraphs - Dobson, Edward; Morris, Joy (The Electronic Journal of Combinatorics, 2009)
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(CD) to be the wreath product of the automorphism groups Aut(C)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 D) is if Aut(C D) eq Aut (C) Aut (D), and in particular, show that in this case there exist vertex-transitive graphs C’ and D’ such that C’ D’ = C D and Aut (CD) = Aut (C’) Aut(D’).