On locating-domination in graphs

Abstract

set D of vertices in a graph G = (V,E) is a locating-dominating set (LDS) if for every two vertices u, v of V D the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The locating-domination number γL(G) is the minimum cardinality of a LDS of G, and the upper locating-domination number, ΓL(G) is the maximum cardinality of a minimal LDS of G. We present different bounds on ΓL(G) and γL(G).