A set W of the vertices of a connected graph G is called a resolving set for G if for every two distinct vertices u, υ ∈ V ( G) there is a vertex w ∈ W such that d( u,w) ≠ d( υ,w). A resolving set of minimum cardinality is called a metric basis for G and the number of vertices in a metric basis is called the metric dimension of G, denoted by dim( G). For a vertex u of G and a subset S of V ( G), the distance between u and S is the number min d( u, s). A k-partition Π = { S, S, ..., S} of V ( G) is called a resolving partition if for every two distinct vertices u, v ∈ V ( G) there is a set S in Π such that d( u, S) ≠ d( v, S). The minimum k for which there is a resolving k-partition of V ( G) is called the partition dimension of G, denoted by pd( G). The circulant graph is a graph with vertex set ℤ, an additive group of integers modulo n, and two vertices labeled i and j adjacent if and only if i − j (mod n) ∈ C, where C ∈ ℤ has the property that C = −C and 0 ∉ C. The circulant graph is denoted by X where Δ = | C|. In this paper, we study the metric dimension of a family of circulant graphs X with connection set $$C = \left\{ {1,\tfrac{n} {2},n - 1} \right\}$$ and prove that dim( X) is independent of choice of n by showing that We also study the partition dimension of a family of circulant graphs X with connection set C = {±1,±2} and prove that pd( X) is independent of choice of n and show that pd( X) = 5 and . [ABSTRACT FROM AUTHOR]