#TITLE_ALTERNATIVE#
For any S V(G) and a vertex v ⊆∈ G, the distance between v and S is d(v, S) = min {d(v, x)| x ∈ S}. For an ordered k-partition Π = {S1, S2,..., Sk} of V(G) and a vertex v of G, the representation of v with respect to Π is the k-vectors r(v| Π)...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/8839 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | For any S V(G) and a vertex v ⊆∈ G, the distance between v and S is d(v, S) = min {d(v, x)| x ∈ S}. For an ordered k-partition Π = {S1, S2,..., Sk} of V(G) and a vertex v of G, the representation of v with respect to Π is the k-vectors r(v| Π) = (d(v, S1), d(v, S2),..., d(v, Sk)). The partition Π is called a resolving partition if the k-vectors r(v| Π), v ∈ V(G) are distinct. The minimum k for which there is a resolving k-partition of V(G) is the partition dimension of G (written pd(G)). This final project determines the partition dimensions of Fan (Fn) and Windmill graphs. Precisely, we find the partition dimensions of Fans (Fn) for 4 ≤ n ≤ 13. |
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