Pelabelan Fibonacci Prima Ke-k Pada Graf H dan Graf Ulat H_n
DOI:
https://doi.org/10.15575/kubik.v8i2.29290Keywords:
bilangan Fibonacci, faktor persekutuan terbesar, graf prima Fibonacci ke-kAbstract
Artikel ini membahas tentang pelabelan Fibonacci prima ke-k pada sebuah graf sederhana G dengan himpunan simpul V(G) dan himpunan sisi E(G). Suatu graf G adalah graf Fibonacci prima ke-k jika terdapat pemetaan injektif f:V(G)→{F_k,F_(k+1),…,F_(k+n-1)} yang memetakan himpunan simpul V(G) ke himpunan bagian bilangan Fibonacci {F_k,F_(k+1),…,F_(k+n-1)}. F_k  merupakan bilangan Fibonacci yang berada pada urutan ke-k dimana k≤n dan k,n∈N. Untuk setiap sisi uv∈E(G) dengan u,v∈V(G)  berlaku f^* (uv)=gcdâ¡(f(u),f(v))=1 dengan f^*:E(G)→N. Graf yang digunakan dalam penelitian ini adalah graf H dengan orde lebih besar atau sama dengan tiga dan graf ulat H_n  dengan orde lebih besar atau sama dengan dua. Penelitian ini bertujuan untuk mengkontruksi pelabelan Fibonacci prima ke-k pada graf H dan graf ulat H_n  serta membuktikan bahwa graf tersebut adalah graf Fibonacci prima ke-k.
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