Siti Aini, - (2024) PELABELAN L(3,1) PADA GRAF LOLLIPOP DAN GRAF HASIL OPERASI COMB ANTARA GRAF BINTANG DAN GRAF SIKLUS. S1 thesis, Universitas Pendidikan Indonesia.
Abstract
Penelitian ini mengkaji pelabelan L(3,1) pada graf Lollipop L_(m,n) dan graf hasil operasi comb antara graf bintang dan graf siklus (S_q⊳C_r). Pelabelan L(3,1) merupakan salah satu jenis pelabelan pada graf yang melibatkan pemberian label pada simpul-simpul graf yang memenuhi aturan |f(u)-f(v)|≥3, jika d(u,v)=1 dan |f(u)-f(v)|≥1, jika d(u,v)=2, untuk u,v∈V(G). Label terbesar dalam pelabelan graf disebut span. Untuk menentukan rumus dalam mencari nilai minimum span pelabelan L(3,1) pada graf Lollipop L_(m,n) dan graf S_q⊳C_r, digunakan metode pendeteksian pola. Metode ini mencari pola nilai minimum label terbesar (span) untuk semua graf Lollipop L_(m,n) serta S_q⊳C_r dengan jumlah simpul tertentu. Selanjutnya rumus tersebut dibuktikan secara matematis. Dari hasil penelitian ini, diperoleh nilai minimum span untuk pelabelan L(3,1) pada graf Lollipop L_(m,n) dengan m≥3 dan n adalah suatu bilangan bulat positif, yaitu λ_3,1 (L_(m,n) )=3m-3. Untuk pelabelan L(3,1) pada graf S_q⊳C_r dengan q≥3 dan r≥3, diperoleh nilai minimum span:
λ_3,1 (S_q⊳C_r )=8,jika q=r=3,
λ_3,1 (S_q⊳C_r )=q+4,jika q≥4 atau r≥4.
This research studies the L(3,1)-labeling on Lollipop graph L_(m,n) and the product of comb operation between star graphs and cycle graphs (S_q⊳C_r). L(3,1)-labeling is a type of labeling on graphs that involves the labeling of the vertices of the graph satisfying the rules |f(u)-f(v)|≥3, if d(u,v)=1 and |f(u)-f(v)|≥1, if d(u,v)=2, for u,v∈V(G). The largest label in a graph labelling is called span. To determine the formula for finding the minimum span value of L(3,1)-labeling in Lollipop graphs L_(m,n) and S_q⊳C_r graphs, the pattern detection method is utilized. This method is used to find the largest minimum label value (span) pattern for all Lollipop graphs L_(m,n) and S_q⊳C_r graphs in a given number of vertices. Furthermore, the formula is proven mathematically. From the result of this research, the minimum span value for L(3,1) labeling on Lollipop graphs L_(m,n) with m≥3 and n is a positif integer, is λ_3,1 (L_(m,n) )=3m-3. For the L(3,1)- labeling on the S_q⊳C_r graphs with q≥3 and r≥3, the minimum span value is:
λ_3,1 (S_q⊳C_r )=8, if q=r=3,
λ_3,1 (S_q⊳C_r )=q+4, if q≥4 or r≥4.
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| Item Type: | Thesis (S1) |
|---|---|
| Additional Information: | https://scholar.google.com/citations?view_op=new_profile&hl=id ID SINTA Dosen Pembimbing: Yaya S. Kusumah: 6676817 Kartika Yulianti: 5979108 |
| Uncontrolled Keywords: | Pelabelan L(3,1), Graf Lollipop, Graf Bintang, Graf Siklus, Operasi Comb, Pelabelan Graf L(3,1)-Labeling, Lollipop Graphs, Star Graphs, Comb Product, Graph Labeling |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1 > Program Studi Matematika (non kependidikan) |
| Depositing User: | Siti Aini |
| Date Deposited: | 07 Sep 2024 03:48 |
| Last Modified: | 07 Sep 2024 03:48 |
| URI: | http://repository.upi.edu/id/eprint/122921 |
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