Partition dimension of rooted product graphs

An ordered k-partition Π={S1,S2,…,Sk} of V(G) is called a resolving partition if for every two distinct vertices u,v ∈ V(G), there exists a set Si in Π such that the distance between u and Si is not equal to the distance between v and Si. The minimum k for which there is a resolving k-partition of V(G) is called the partition dimension of G. In this paper, we provide the tight bounds for the partition dimension of rooted product graphs. Further, partition dimension of particular class of rooted product graphs has been studied.