ABSTRAK
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−generateddigraph Cayley yang tidak memi-liki path Hamilton, seperti bahwa perintah generatorai danbi yang tak terbatas. Dibuktikan bahwa jika G adalah kelompok terbatas dengan | [G, G] |≤ 3, maka setiap digraph Cayley yang terhubung pada Gmemiliki path Hamilton.
Kata kunci: Digraph, Digraph Cayley, path Hamilton.
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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−generatedCayley digraphs that do not have Hamiltonian paths, such that the orders of the generatorsai andbi are unbounded. We also prove that ifGis any finite group with|[G, G]|≤ 3, then every connected Cayley digraph on G has a hamiltonian path.
Keyword: Digraph, Cayley digraph, path Hamilton
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