2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115040We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph K_{s,t} which admits only the identity automorphism. In particular this allows us to determine the distinguishing number of the Cartesian product of complete graphs.11 pages. Submitted for publicationCombinatorics05C25text