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For a vertex v of a connected graph G and a subset S of V (G), the distance between v and S is dIt is shown that the partition dimension of a graph G is bounded above by 1 more than its metric dimension. An upper bound for the partition dimension of a bipartite graph G is given in terms of the cardinalities of its partite sets, and it is shown that the bound is attained if and only if G is a complete bipartite graph. Graphs of order n having partition dimension 2, n, or n − 1 are characterized.Mathematics Subject Classification (1991). 05C12.
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