Path Hamilton pada Digraph Cayley

Abstract

This paper is a descriptive-qualitative research methods literature (library research) research that examines the literature, especially on digraph Cayley for the purpose of collecting data and information with the help of a variety of materials such as books and documents. In this paper will be discuss about The study of Hamilton paths in Cayley digraphs has had a long history. We construct an infinite fa- mily Cay(Gi; ai; bi) of connected, 2−generated Cayley digraphs that do not have Hamiltonian paths, such that the orders of the generators ai and bi are unbounded. We also prove that if G is any finite group with | [G,G] | 3, then every connected Cayley digraph on G has a hamiltonian path.

Tesis ini merupakan penelitian deskriptif-kualitatif dengan menggunakan metode penelitian kepustakaan (library research) yaitu penelitian yang mengkaji secara kepustakaan, khususnya tentang digraph Cayley. Dalam tesis ini mengkaji ten- tang lintasan Hamilton di digraph Cayley. Dibangun sebuah keluarga yang tak terbatas Cay(Gi; ai; bi) terhubung, 2−generated digraph Cayley yang tidak memi- liki path Hamilton, seperti bahwa perintah generator ai dan bi yang tak terbatas. Dibuktikan bahwa jika G adalah kelompok terbatas dengan | [G,G] | 3, maka setiap digraph Cayley yang terhubung pada G memiliki path Hamilton.