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# Characterization of n-vertex graphs with metric dimension n - 3

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W) := (d(v, w1), d(v, w2), . . . , d(v, wk)) is called the metric representation of v with respect to W, where d(x, y) is the distance between vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W. The …