Locating domination in bipartite graphs and their complements
Carmen Hernando, Mercè Ferrater Mora, Ignacio M. Pelayo · RECERCAT (Consorci de Serveis Universitaris de Catalunya) · 2017
A set S of vertices of a graph G is distinguishing if the sets of neighbors in S for every pair of vertices not in S are distinct. A locating-dominating set of G is a dominating distinguishing set. The location-domination number of G , ¿ ( G ), is the minimum cardinality of a locating-dominating set. In this work we study relationships between ¿ ( G ) and ¿ ( G ) for bipartite graphs. The main result is the characterization of all connected bipartite graphs G satisfying ¿ ( G ) = ¿ ( G ) + 1. To this aim, we define an edge-labeled graph G S associated with a distinguishing set S that turns out to be very helpful