Identifying codes of Cartesian product of two cliques of the same size (Q1010656)

Summary: We determine the minimum cardinality of an identifying code of \(K_n\square K_n\), the Cartesian product of two cliques of same size. Moreover we show that this code is unique, up to row and column permutations, when \(n\geq 5\) is odd. If \(n\geq 4\) is even, we exhibit two distinct optimal identifying codes.