Locating-dominating set

Locating-dominating set --- размещённое доминирующее множество.

Slater (1987) defined a locating-dominating set, denoted by an LD-set, in a connected graph [math]\displaystyle{ G }[/math] to be a dominating set [math]\displaystyle{ D }[/math] of [math]\displaystyle{ G }[/math] such that for every two vertices [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math] in [math]\displaystyle{ V(G) - D }[/math], [math]\displaystyle{ N(u) \cap D \neq N(v) \cap D }[/math]. The location-domination number [math]\displaystyle{ \gamma_{L}(G) }[/math] is the minimum cardinality of an LD-set for [math]\displaystyle{ G }[/math].