Detailed Definition
For an ordered subset of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple, where d(x,y) represents the distance between the vertices x and y. The set W is a resolving set (or locating set) for G if every two vertices of G have distinct representations. The metric dimension of G is the minimum cardinality of a resolving set for G. A resolving set containing a minimum number of vertices is called a basis (or reference set) for G. Resolving sets were introduced independently by Slater (1975) and Harary & Melter (1976).
Read more about this topic: Metric Dimension (graph Theory)
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