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On the k partition dimension of graphs

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Figure 1: A graph G with ς(G) = 3. The vertices belonging to M(G) are depicted in black while the terminal vertices are represented in gray.
Figure 2: The set Π = {{1}, {2}{3, 4, 5, 6, 7, 8}, {9}, {10}} is a 2-partition basis of this T and |Π| = 5 = dim 2 (T ) + 1.
Figure 3: In this tree T we have that M i (T ) = {i} for i ∈ {1, 2, 3}, l 1 = 1, l 2 = 2, l 3 = 3, t 1 = 3, t 2 = 4, t 3 = 5

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