  An identifying code in a graph is a dominating set that also has the property
that the closed neighborhood of each vertex in the graph has a distinct
intersection with the set. It was recently shown by Gravier, Moncel and Semri
that the minimum cardinality of an identifying code for the Cartesian product
of two cliques of the same order n is the floor of 3n/2. We consider
identifying codes of the direct product of two cliques. In particular, we
answer a question of Klavzar and determine the minimum cardinality of an
identifying code for the direct product of any two cliques.
