The Partition Dimension of Daisy Graphs and Its Barbell

The partition dimension of a graph is determined by minimum number of vertex partitions such that every vertex has different distances to the ordered partitions. A complete graph is very easy to determine its partition dimension because each vertex has the same distance to other vertices. However, what are the partition dimension if a complete graph is modified so that it becomes a daisy graph. In this paper, we discuss the partition dimension of daisy graphs. Next, we will also provide barbell graph operations on daisy graphs.