On the bounded partition dimension of some classes of convex polytopes

Let G be a connected graph with V(G) and E(G) be the vertex set and edge set. For a vertex u is an element of V(G) and a subset W subset of V(G), the distance between u and W is d(u,W) = min{d(u,x): x is an element of W}. Let Pi={W-1, W-2, W-3, ...,W-t}be an ordered t-partition of V(G), the representation of v with respect to Pi is the t-vector r(nu vertical bar Pi) = (d(nu,W-1), d(upsilon,W-2),d(upsilon,W-3), ...,d(upsilon,W-t)). If the representations of the all vertices of G with respect to Pi are distinct, then t-partition Pi is a resolving partition. The minimum t for which there is a resolving t-partition of V(G) is the partition dimension pd(G) of G. In this paper, we determined the upper bound of partition dimension for convex polytopes.