Partition Dimension of Some Classes of Trees

Chartrand, E. Salehi and P. Zhang (1998) studied the concept of graph partition dimension as a new approach to settle the problem of finding the metric dimension of a graph. Now, the partition dimensions of many classes of trees have been known. However, there are the partition dimension of a general tree is still not completely solved. In this paper, we study the partition dimension on some specific classes of trees. In particular, we characterize all caterpillars and a subdivision of a star having partition dimension four.