A vertex x in a digraph D is said to resolve a pair u, v of vertices of D if the distance from u to x does not equal the distance from v to x. A set S of vertices of D is a resolving set for D if every pair of vertices of D is resolved by some vertex of S. The smallest cardinality of a resolving set for D, denoted by dim(D), is called the metric dimension for D. Sharp upper and lower bounds for the metric dimension of the Cayley digraphs Cay( : ), where is the group Z n 1 ⊕ Z n 2 ⊕ · · · ⊕ Z n m and is the canonical set of generators, are established. The exact value for the metric dimension of Cay({(0, 1), (1, 0)} : Z n ⊕ Z m ) is found. Moreover, the metric dimension of the Cayley digraph of the dihedral group D n of order 2n with a minimum set of generators is established. The metric dimension of a (di)graph is formulated as an integer programme. The corresponding linear programming formulation naturally gives rise to a fractional version of the metric dimension of a (di)graph. The fractional dual implies an integer dual for the metric dimension of a (di)graph which is referred to as the metric independence of the (di)graph. The metric independence of a (di)graph is the maximum number of pairs of vertices such that no two pairs are resolved by the same vertex. The metric independence of the n-cube and the Cayley digraph Cay( : D n ), where is a minimum set of generators for D n , are established.
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