The connected partition dimension of truncated wheels

Abstract

Let G be a connected graph. For a vertex v of G and a subset S of V(G), the distance between v and S is d(v, S) = min Given an ordered k-partition = of V(G), the representation of v with respect to is the k-vector If for each pair of distinct vertices then the k-partition is said to be a resolving partition. The partition dimension of G, denoted by pd(G), is determined by the minimum k for which there is a resolving partition of V(G). If each induced subgraph for Si, is connected in G, then the resolving partition = of V(G) is said to be connected. The connected partition dimension of G, denoted by cpd(G), is determined by the minimum k for which there is a connected resolving partition of V(G). In this paper, we compute the connected partition dimension of the truncated wheels TWn. It is shown that for any natural number the connected partition dimension of the truncated wheel TWn is 3 when n = 3 and when

Keywords

• partite set
• resolving partition
• connected partition dimension