On the bounded partition dimension of some classes of convex polytopes

Abstract

Let G be a connected graph with V(G) and E(G) be the vertex set and edge set. For a vertex u ∈ V(G) and a subset W ⊂ V(G), the distance between u and W is (u, W)=min {d(u, x): x ∈ W}. Let ∏ ={ W1, W2, W3, … , Wt} be an ordered t-partition of V(G), the representation of v with respect to ∏ is the t-vector . If the representations of the all vertices of G with respect to ∏ are distinct, then t-partition ∏ 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.

Topics & Concepts