The distinguishing number of a graph G, denoted D(G), is the minimum number of colors such that there exists a coloring of the vertices of G where no nontrivial graph automorphism is color-preserving. In this paper, we answer an open question posed in Bogstad and Cowen [The distinguishing number of the hypercube, Discrete Math. 283 (2004) 29-35] by showing that the distinguishing number of Q"n^p, the pth graph power of the n-dimensional hypercube, is 2 whenever 2=4. The sequence of distinguishing numbers {D(AQ"n)}"n"="1^~ answers a question raised in Albertson and Collins [An introduction to symmetry breaking in graphs, Graph Theory Notes N.Y. 30 (1996) 6-7].
['Melody Chan']
Note: The distinguishing number of the augmented cube and hypercube powers