DIMENSI METRIK PADA GRAF AMALGAMASI TANGGA SEGITIGA DIPERUMUM HOMOGEN
DOI:
https://doi.org/10.25077/jmu.8.1.84-90.2019Abstract
Misalkan terdapat G = (V, E) suatu graf terhubung dan misal terdapat dua titik u, v ∈ V . Jarak antara u dan v didefinisikan sebagai panjang lintasan terpendek antara u dan v yang dinotasikan dengan d(u, v). Misalkan terdapat himpunan terurut W ⊂ V (G), dengan W = {w1, w2, · · · , wk}. Misal terdapat titik v ∈ V (G). Representasi titik v terhadap W, dinotasikan 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 dinamakan sebagai himpunan pemisah (resolving set) untuk G. Himpunan pemisah yang mempunyai kardinalitas minimum dinamakan himpunan pemisah minimum (minimum resolving set). Banyaknya anggota dari himpunan pemisah minimum ini dinamakan dimensi metrik dari G, dinotasikan dim(G). Graf amalgamasi graf tangga segitiga diperumum homogen adalah graf yang diperoleh dari hasil amalgamasi m buah graf tangga segitiga diperumum yang homogen, lebih sederhana dinotasikan dengan Amal{T rn, v}m. Pada paper ini dibahas dimensi metrik dari Amal{T rn, v}m dengan n = 3,n = 4 dan m = 2
kata kunci: Dimensi Metrik, Himpunan pemisah,Representasi, Graf amalgamasi tangga segitiga diperumum homogen.
Diterima: Direvisi:
Dipublikasikan : Kata
Kunci: Dimensi Metrik, Himpunan pemisah,Representasi, Graf amalgamsi tangga segitiga diperumum homogen.
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