On global location-domination in bipartite graphs

A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locatingdominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number λ(G). An LD-set S of a graph G is global if it is an LD-set of both G and its complement G. The global location-domination number λg(G) is the minimum cardinality of a global LD-set of G. For any LD-set S of a given graph G, the so-called S-associated graph G is introduced. This edge-labeled bipartite graph turns out to be very helpful to approach the study of LD-sets in graphs, particularly when G is bipartite. This paper is mainly devoted to the study of relationships between global LD-sets, LD-codes and the location-domination number in a graph G and its complement G, when G is bipartite.