Partition dimension of trees - palm approach

Hafidh, Yusuf (Department of Mathematics, Institut Teknologi Bandung)
Baskoro, Edy Tri (Department of Mathematics, Institut Teknologi Bandung)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications

The partition dimension of a graph is the minimum number of vertex partitions such that every vertex has different distances to the ordered partitions. Many resolving partitions for trees have all vertices not in an end-path in the same partition. This reduces the problem of the partition dimension of trees into finding the partition dimension of palms, the end-paths from a branch. In this paper, we construct a resolving partition for trees using resolving partitions of their palms. We also study some bounds for the partition dimension of palms and also find the partition dimension of regular palm and olive trees.