Pelabelan-L(2,1) pada Graf Hasil Operasi Comb antara Graf Lintasan dan Graf Bintang

Putri, Anissa Zarah Anindita (2017) Pelabelan-L(2,1) pada Graf Hasil Operasi Comb antara Graf Lintasan dan Graf Bintang. Diploma thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

INDONESIA : Misalkan G adalah graf dengan p titik dan q sisi. Pelabelan-L(2,1) pada graf G adalah fungsi f:V→{0,1,2,3,…,k} sedemikian sehingga memenuhi kondisi |f(x)-f(y)|≥2, jika d(x,y)=1 dan |f(x)-f(y)|≥1, jika d(x,y)=2. Bilangan pelabelan-L(2,1)dari G, dinotasikan dengan λ(G), adalah nilai k terkecil sehingga G memiliki pelabelan-L(2,1) dengan label terbesar k. Graf P_n ⊳_u S_m adalah graf yang diperoleh dengan mengambil satu duplikat dari P_n dan |V(P_n)| duplikat dari S_m dan menempelkan titik u dari masing-masing graf S_m salinan ke-i pada titik ke-i dari graf P_n. Pada skripsi ini, diperoleh nilai pelabelan-L(2,1) sehingga graf P_n ⊳_u S_m dapat dilabeli dengan pelabelan-L(2,1). Kata kunci: Graf lintasan, Graf bintang, Graf hasil kali comb, Pelabelan graf, Pelabelan-L(2,1), Bilangan-λ. ENGLISH : Let G be a graph with p vertices and q edges. An L(2,1)-labeling of graph G is a function f:V→{0,1,2,3,…,k} such that satisfies the conditions |f(x)-f(y)|≥2, if d(x,y)=1 and |f(x)-f(y)|≥1, if d(x,y)=2. The L(2,1)-labeling number of G, denoted by λ(G), is the smallest number k such that G has a L(2,1)-labeling with the largest label k. Graph P_n ⊳_u S_m, is a graph obtained by taking one copy of P_n and |V(P_n)| copies of S_m and grafting the i-th copy of S_m at the vertex u to the i-th vertex of P_n. In this undergraduate thesis, determained L(2,1)-labeling number such that graph P_n ⊳_u S_m can be labeled with L(2,1)-labeling. Keywords:Path graph, Star graph, Comb product graph, Graph labeling, L(2,1)-labeling, λ-numb.

Item Type: Thesis (Diploma)
Uncontrolled Keywords: Graf lintasan; Graf bintang; Graf hasil kali comb; Pelabelan graf; Pelabelan-L(2,1); Bilangan-λ.
Subjects: Mathematics > Mathematicians
Analysis, Theory of Functions > Special Functions
Applied mathematics > Game Theory Mathematics
Divisions: Fakultas Sains dan Teknologi > Program Studi Matematika
Depositing User: Anissa Zarah Anindita Putri
Date Deposited: 26 Nov 2020 04:33
Last Modified: 26 Nov 2020 04:33
URI: https://digilib.uinsgd.ac.id/id/eprint/28778

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