DIMENSI METRIK DARI GRAF SPINNER (C3 × P2) Kn UNTUK n = 1
DOI:
https://doi.org/10.25077/jmu.7.4.1-6.2018Abstract
Misalkan u dan v adalah titik-titik dalam graf terhubung G. Jarak d(u, v) adalah panjang lintasan terpendek antara u dan v pada graf G. Bila diberikan himpunan terurut W = {w1, w2, w3, · · · , wk} dari titik-titik dalam graf terhubung G dan titik v ∈ V (G), representasi dari v terhadap W adalah k-vektor yang dapat ditulis dengan r(v|W) = (d(v, w1), d(v, w2), · · · , d(v, wk)). Jika r(v|W) untuk setiap titik v ∈ (G) berbeda, maka W disebut himpunan pembeda dari V (G). Himpunan pembeda dengan kardinalitas minimum disebut himpunan pembeda minimum dan kardinalitas dari basis metrik tersebut dinamakan dimensi metrik dari graf G dan dinotasikan dengan dim(G). Graf spinner adalah perkalian kartesius antara graf C3 dan graf P2 yang menghasilkan graf C3 × P2, kemudian graf C3 × P2 tersebut dikoronakan dengan graf komplemen Kn yaitu Kn, sehingga graf spinner tersebut dapat dinotasikan dengan (C3 ×P2)Kn. Pada paper ini akan dibahas dimensi metrik dari graf spinner (C3 × P2) Kn untuk n = 1.
Kata Kunci: Dimensi metrik, Himpunan pembeda, Representasi, Hasilkali kartesius, Graf korona
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