DIMENSI METRIK DARI GRAF Amal(T rn, v)m untuk n = 5 dan m = 3
DOI:
https://doi.org/10.25077/jmu.8.4.77-84.2019Abstract
Misalkan terdapat graf terhubung G = (V, E) dan himpunan terurut W ⊂ V (G), dengan W = {w1, w2, . . . , wk}, serta terdapat titik v ∈ V (G). Representasi titik v terhadap W yang dinotasikan dengan r(v|W), adalah k-vektor
r(v|W) = (d(v, w1), d(v, w2), . . . , d(v, wk)).
Jika untuk setiap dua titik u dan v di G diperoleh bahwa r(u|W) 6= r(v|W), maka W disebut sebagai himpunan pemisah (resolving set) untuk graf G. Kardinalitas dari himpunan pemisah minimum dinamakan dimensi metrik dari graf G yang dinotasikan dim(G). Graf amalgamasi tangga segitiga diperumum homogen adalah graf yang diperoleh dari hasil amalgamasi graf tangga segitiga diperumum yang sama untuk masing-masing graf. Graf tangga segitiga diperumum dinotasikan dengan T rn, untuk n ≥ 2. Pada paper ini dibahas tentang dimensi metrik dari graf Amal(T rn, v)m untuk n = 5 dan m = 3.
Kata Kunci: Dimensi metrik, Himpunan pemisah, Graf Amal(T rn, v)m
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