Pelabelan Rata-Rata Titik Ganjil dan Genap pada \(P_p\) dan \(C_p\)

Hafeni, Nabila Almafelia (2017) Pelabelan Rata-Rata Titik Ganjil dan Genap pada \(P_p\) dan \(C_p\). Sarjana thesis, Uin Sunan Gunung Djati Bandung.

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Abstract

Nama: Nabila Almafelia Hafeni NIM: 1137010041 Judul: Pelabelan Rata-Rata Titik Ganjil dan Genap pada \(P_n\), \(C_n\), dan \(P_m\) Dari sekian banyak topik pada teori graf, pelabelan merupakan salah satu topik yang sangat luas pengembangannya. Pelabelan graf merupakan penetapan bilangan-bilangan bulat ke titik, sisi atau keduanya pada suatu graf berdasarkan kondisi tertentu. Pelabelan rata-rata titik ganjil dan genap, merupakan kajian pada pelabelan graf. Suatu graf \(G\) dengan \(q\) sisi merupakan graf rata-rata titik ganjil jika \(f:V(G)\rightarrow\{1,3,5,\ldots,2q-1\}\) dan \(f\) merupakan fungsi satu-satu, sedemikian sehingga jika sisi \(uv\) dilabeli dengan \(\frac{f(u)+f(v)}{2}\) maka label sisi yang dihasilkan berbeda. Kemudian suatu graf \(G\) dengan \(q\) sisi merupakan graf rata-rata titik genap jika \(f:V(G)\rightarrow\{2,4,6,\ldots,2q\}\) dan \(f\) adalah injektif fungsi, such that when each edge \(uv\) is labeled with \(\frac{f(u)+f(v)}{2}\) maka label sisi yang dihasilkan berbeda. \(P_n\), \(C_n\), dan \(P_m\) merupakan graf rata-rata titik ganjil dan genap, karena graf tersebut dapat dilabeli dengan pelabelan rata-rata titik ganjil dan genap yang akan dikaji pada distribusi ini. Kata kunci: Graf Rata-Rata Titik Ganjil dan Genap, Pelabelan Rata-Rata Titik Ganjil dan Genap, \(P_n\), \(C_n\), \(P_m\). Name: Nabila Almafelia Hafeni NIM: 1137010041 Title: Vertex Odd and Even Mean Labelling of \(P_n\), \(P_m\), and \(C_n\) Labelling, one of the topics in graph theory, is the most extensive topics of knowledge in graph theory. Graph labeling is a mapping of integers to vertices, edges, or both of them on a graph based on certain conditions. Vertex odd and even mean labeling, which leads the study of graph labeling. A graph \(G\) with \(q\) edges to be a vertex odd mean graph if \(f:V(G)\rightarrow\{1,3,5,\ldots,2q-1\}\) and \(f\) is an injective function, such that when each edge \(uv\) is labeled with \(\frac{f(u)+f(v)}{2}\) then the resulting edges are distinct. Then a graph \(G\) with \(q\) edges to be a vertex even mean graph if \(f:V(G)\rightarrow\{2,4,6,\ldots,2q\}\) and \(f\) is an injective function, such that when each edge \(uv\) is labeled with \(\frac{f(u)+f(v)}{2}\) then the labels of edges are distinct. \(P_n\), \(P_m\), and \(C_n\) are vertex odd and even mean graphs, because the graph can be labeled by vertex odd and even mean labeling that will be investigated in this undergraduate thesis. Keywords: Vertex Odd and Even Mean Graph, Vertex Odd and Even Mean Labeling, \(P_n\), \(P_m\), \(C_n\).

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