Geodesic
On locating-domination in graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 223-235

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A 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 γ_L(G) is the minimum cardinality of a LDS of G, and the upper locating-domination number, Γ_L(G) is the maximum cardinality of a minimal LDS of G. We present different bounds on Γ_L(G) and γ_L(G).
Keywords: upper locating-domination number, locating-domination number 
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Chellali, Mustapha; Mimouni, Malika; Slater, Peter. On locating-domination in graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 223-235. http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a2/