On separating systems of graphs

Given a finite loopless graph G (resp. digraph D), let @s(G), @f(G) and @j(D) denote the minimal cardinalities of a completely separating system of G, a separating system of G and a separating system of D, respectively. The main results of this paper are: @d(G) = minm^m"@?"m"/"2"@?>=@c(G)and @f(G) = @?log"2 @c(G)@? where @c(G) denotes the chromatic number of G. (ii) All the problems of determining @s(G), @f(G) and @j(D) are NP-complete.