On the Partition Dimension of Circulant Graphs.

For a vertex v of a connected graph G (V, E) and a subset S of V, the distance between v and S is defined by d(v,S) = mind{d(v,x): x ∈ S}. For an ordered k-partition π = {S1, SS2, ...,S2..., S k} of V, the representation of v with respect to π is the k-vector r(v|π} = (d(v,S1), d(v,S2, ..., d (v,Sk. The k-partition π is a resolving partition if the k-vectors r(v|π ), v V∈ V are distinct. The minimum k for which there is a resolving k-partition of V is the partition dimension of G. In this paper, we obtain the partition dimension of circulant graphs G - C (n, ± {1,2,...,j}), 1 < j <[n/2], n ≥ (j+k) (j+1) and n = k (mod 2j) as, Pd (G) = j + 1{when j is even and ged (k,2j) = 1,/when j is odd and k = 2m, 1 ≤ m ≤ j. [ABSTRACT FROM AUTHOR]