PELABELAN TITIK L(3,1) PADA GRAF SUPERCYCLE

Fanny Febriyani, - (2023) PELABELAN TITIK L(3,1) PADA GRAF SUPERCYCLE. S1 thesis, Universitas Pendidikan Indonesia.

Abstract

Pelabelan L(3,1) didefinisikasn sebagai pemetaan himpunan titik pada graf G ke bilangan bulat non negative untuk setiap 2 titik u,v maka berlaku |f(u)-f(v)|≥3 jika d(u,v)=1 dan |f(u)-f(v)|≥1 jika d(u,v)=2. Permasalahan pelabelan ini dapat diterapkan pada graf khusus yang disebut graf supercycle, yang merupakan hasil dari penggabungan dua buah graf khusus, yaitu graf cycle dan graf Hanoi. Untuk menentukan rumus dalam mencari nilai minimal pelabelan terbesar (span) dari pelabelan L(3,1) pada graf supercycle, dapat menggunakan metode pendeteksian pola. Metode ini mencari pola nilai minimal label terbesar (span) untuk semua graf supercycle dengan jumlah titik tertentu. Hasil penelitian ini diperoleh nilai minimal label terbesar (span) untuk r=1 pada graf supercycle Sc(n,r) adalah:
λ_3,1 (Sc(n,r)) = 6 jika n=1,
λ_3,1 (Sc(n,r)) = 7 jika n>1, n bilangan genap
λ_3,1 (Sc(n,r)) = 8 jika n>1, n bilangan ganjil
Untuk r>1 , diperoleh nilai minimal label terbesar (span) dari pelabelan titik L(3,1) pada graf supercycle Sc(n,r) untuk r>1 adalah
λ_3,1 (Sc(n,r))=8
The L(3,1) labelling is defined as a mapping of a set of points in graph G to non-negative integers, where for any 2 points u,v, such that |f(u)-f(v)|≥3 if d(u,v)=1 and |f(u)-f(v)|≥1 if d(u,v)=2. This labelling problem can be applied to a special type of graph known as a supercycle, which is obtained by combining two specific graphs, namely the cycle graph and the Hanoi graph. To determine the formula for finding the minimum value of the largest label (span) value of L(3,1) labelling on the supercycle graph, the pattern detection method can be utilized. This method finds the patterns of the minimum value of the largest label (span) for all supercycle graphs with a certain number of nodes. The results of this research obtained the minimum value of the largest label (span) for r=1 on the supercycle graph Sc(n,r) is:
λ_3,1 (Sc(n,r)) = 6 if n=1,
λ_3,1 (Sc(n,r)) = 7 if n>1, n even number
λ_3,1 (Sc(n,r)) = 8 if n>1, n odd number
For r>1 , the minimum value of the largest label (span) of the point labelling L(3,1) on the supercycle graph Sc(n,r) obtained:
λ_3,1 (Sc(n,r))=8

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Official URL: http://repository.upi.edu
Item Type: Thesis (S1)
Additional Information: ID Sinta Dosen Pembimbing: 6676817 YAYA S. KUSUMAH 5979108 KARTIKA YULIANTI
Uncontrolled Keywords: Pelabelan L(3,1), Graf Supercycle, Pelabelan Graf, Teori Graf, L(3,1) Labelling, Supercycle Graphs, Graph Labelling, Graph Theory
Subjects: L Education > L Education (General)
Q Science > QA Mathematics
Divisions: Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1 > Program Studi Matematika (non kependidikan)
Depositing User: Fanny Febriyani
Date Deposited: 07 Sep 2023 02:08
Last Modified: 07 Sep 2023 02:08
URI: http://repository.upi.edu/id/eprint/101747

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