A set
S of vertices of a graph
G is \emph{distinguishing} if the sets of neighbors in
S for every pair of vertices not in
S are distinct. A \emph{locating-dominating set} of
G is a dominating distinguishing set. The \emph{location-domination number} of
G,
, is the minimum cardinality of a locating-dominating set. In this work we study relationships between
... [Show full abstract] and for bipartite graphs. The main result is the characterization of all connected bipartite graphs G satisfying . To this aim, we define an edge-labeled graph associated with a distinguishing set S that turns out to be very helpful.