Discriminating codes in (bipartite) planar graphs

Consider a connected undirected bipartite graph G = ( V = I ∪ A , E ) , with no edges inside I or A . For any vertex v ∈ V , let N ( v ) be the set of neighbours of v . A code C ⊆ A is said to be discriminating if all the sets N ( i ) ∩ C , i ∈ I , are nonempty and distinct. dy some properties of discriminating codes in particular classes of bipartite graphs, namely trees and, more generally, (bipartite) planar graphs.