Partition Dimension of Some Classes of Homogenous Disconnected Graphs

An ordered partition Π of the vertex-set resolves a (not necessarily connected) graph G if the representations of all vertices are distinct. The minimum k such that there is a resolving k-partition Π of G is called the partition dimension of G, and denoted by pd(G) or pdd(G) for a connected or a disconnected G, respectively. In this paper, we determine the partition dimension of some homogenous disconnected graphs, namely a disjoint union of stars, double stars and some cycles.