Some trees with partition dimension three
Ketut Queena Fredlina, Edy Tri Baskoro · AIP conference proceedings · 2016
The concept of partition dimension of a graph was introduced by Chartrand, E. Salehi and P. Zhang (1998) [2]. Let G(V, E) be a connected graph. For S ⊆ V (G) and v ∈ V (G), define the distance d(v, S) from v to S is min{d(v, x)|x ∈ S}. Let Π be an ordered partition of V (G) and Π = {S1, S2, ···, Sk }. The representation r(v|Π) of vertex v with respect to Π is (d(v, S1), d(v, S2), ···, d(v, Sk)). If the representations of all vertices are distinct, then the partition Π is called a resolving partition of G. The partition dimension of G is the minimum k such that G has a resolving partition with k partition classes. In this paper, we characterize some classes of trees with partition dimension three, namely olive trees, weeds, and centipedes.