The Partition Dimension of Some Families of Trees

In 1998, Chartrand, E. Salehi and P. Zhang introduced the concept of graph partition dimension. This is a variant of graph metric dimension concept introduced independently by Slater in 1975 and Harary & Melter in 1976. In this paper, we determine the partition dimension of specific classes of trees, namely homogeneous caterpillars and homogeneous banana trees. In particular, we characterize all trees in these classes with partition dimension three.