The partition dimension of the corona product of two graphs

Let G(V, E) be a connected graph. For a vertex v ∈ V(G) and a subset S of V(G), the distance d(v, S) from v to S is min{d(v, w){pipe} w ∈ S}. For an ordered k-partition Π = {S ₁, S ₂,..., S _k} of V(G), the representation of v with respect to Π is r(v {pipe} Π) = (d(v, S ₁), d(v, S ₂),..., d(v, S _k)). The k-partition Π is called a resolving partition of G if all r(v {pipe} Π) for all v ∈V(G) are distinct. The partition dimension of a graph G is the smallest k such that G has a resolving k-partition. In this paper, we derive an upper bound of the partition dimension of the corona product G ⊙ H, where G, H are connected graphs and the diameter of H is at most 2. Furthermore, we also determine the exact value of the partition dimension of this corona product if G is either a path or a complete graph and H is a complete graph.