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The distance ( , V) between two distinct vertices and V in a graph is the length of a shortest ( , V)-path in . For an ordered subset = { 1 , 2 , . . . , } of vertices and a vertex V in , the code of V with respect to is the ordered -tupleis a resolving set for if every two vertices of have distinct codes. The metric dimension of is the minimum cardinality of a resolving set of . In this paper, we first extend the results of the metric dimension of ( , 3) and ( , 4) and study bounds on the metric dimension of the families of the generalized Petersen graphs (2 , ) and (3 , ). The obtained results mean that these families of graphs have constant metric dimension.

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