Identifying codes of Cartesian product of two cliques of the same size

Abstract

We determine the minimum cardinality of an identifying code of K n□Kn, 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 ≥ 5 is odd. If n ≥ 4 is even, we exhibit two distinct optimal identifying codes.