Locating domination in graphs and their complements
Carmen Hernando, Mercè Ferrater Mora, Ignacio M. Pelayo · RECERCAT (Consorci de Serveis Universitaris de Catalunya) · 2013
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 . Locating-dominating sets of minimum cardinality are called LD -codes and the cardinality of an LD-code is the location-domination number . An LD-set of a graph G is global if S is an LD-set of both G and its complement, G . In this work, we give some relations between the locating-dominating sets and location-domination number in a graph and its complement