Alfiyani, Anisa Saverina (2020) Pelabelan Prima Lingkungan Tertutup Bersama Graf Terkait Roda. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Diberikan graf terhubung $G=(V(G),E(G))$ dengan $n$ simpul. Suatu fungsi bijektif $f:V(G)\rightarrow \{1,2,3,...,n\}$ dikatakan pelabelan prima jika untuk setiap dua simpul berbeda $u, v \in V(G)$ dengan $u$ bertetangga dengan $v$, $gcd\{f(u),f(v)\} = 1$. Graf $G$ dikatakan memiliki pelabelan prima lingkungan jika terdapat suatu pemetaan bijektif $f: V(G)\rightarrow \lbrace 1,2,3,...,n\rbrace$ sedemikian hingga untuk setiap $v\in V(G)$ dengan $deg(v)>1$, $gcd\{ f(u):u\in N(v)\} = 1$. Pada Tugas Akhir ini, diperkenalkan jenis pelabelan baru yaitu pelabelan prima lingkungan tertutup bersama. Graf $G$ dikatakan memiliki pelabelan prima lingkungan tertutup bersama jika terdapat fungsi bijektif $f:V(G) \rightarrow \{ 1,2,...,n \}$ sedemikian hingga untuk setiap dua simpul berbeda $u, v \in V(G)$ dengan $u$ bertetangga dengan $v$, $gcd \{ f(w):w\in N[u,v]\} =1$. Dalam Tugas Akhir ini juga dibuktikan bahwa graf dasar dan beberapa graf terkait roda merupakan graf prima lingkungan tertutup bersama, dengan memberikan langkah-langkah (algoritma) untuk mendapatkan pelabelan prima lingkungan bersama pada graf tersebut.
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Let $G=(V(G), E(G))$ be a connected graph with $n$ vertices. A bijection $f:V(G)\rightarrow \{1, 2, 3, ..., n\}$ is said to be prime labeling if for each two distinct vertices $u, v \in V(G)$ which $u$ is adjacent to $v$, $gcd\{f(u),f(v)\}=1$. A graph $G$ is called neighbourhood prime if there is a bijection $f:V(G)\rightarrow \{1, 2, 3, ..., n\}$ so that for each vertex $v\in V(G)$ with $deg(v)>1$, $gcd\{f(u):u\in N(v)\}=1$. In this Final Project, author introduces a new type of labeling called common closed neighbourhood prime labeling. A graph $G$ is called common closed neighbourhood prime if there is a bijection $f:V(G) \rightarrow \{ 1,2,...,n \}$ so that for each two distinct vertices $u, v \in V(G)$ which $u$ is adjacent to $v$, $gcd \{ f(w):w\in N[u,v]\} =1$. Author proved that basic graphs and wheel related graphs are common closed neighbourhood prime graphs, by providing steps algorithms to obtain the common closed neighbourhood prime labeling.
| Item Type: | Thesis (Other) |
|---|---|
| Additional Information: | RSMa 511.5 Alf p-1 • Alfiyani, Anisa Saverina |
| Uncontrolled Keywords: | Pelabelan prima, Pelabelan prima lingkungan, Pelabelan prima lingkungan tertutup bersama, Graf terkait roda. |
| Subjects: | Q Science > QA Mathematics > QA166 Graph theory |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Anisa Saverina Alfiyani |
| Date Deposited: | 23 Aug 2020 05:51 |
| Last Modified: | 05 Nov 2023 16:02 |
| URI: | http://repository.its.ac.id/id/eprint/79390 |
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