Sifat hamiltonian dan hipohamiltonian pada graf Petersen Diperumun (GR_{n,1} & GP_{n,2})

Danarto, Imam (2012) Sifat hamiltonian dan hipohamiltonian pada graf Petersen Diperumun (GR_{n,1} & GP_{n,2}). Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA :

Di dalam teori graf terdapat beberapa sifat keterhubungan, yaitu sifat Hamiltonian dan Hipohamiltonian. Graf Hamiltonian adalah sikel yang melalui masing-masing titik tepat satu kali. Sehingga suatu graf dikatakan mempunyai sifat Hamiltonian jika titik awal sama dengan titik akhir, dengan melalui masing- masing titik tepat satu kali. Graf Hipohamiltonian adalah jika bukan graf Hamiltonian, tetapi jika dihapus salah satu titik membentuk graf Hamiltonian. Graf Petersen adalah graf kubik dengan 10 titik, 15 sisi dan setiap titik berderajat tiga. Graf Petersen diperumum dinotasikan GP_{n,k} , untuk bilangan positif n dan k dengan 2 ≤ 2k < n. Graf Petersen tidak Hamiltonian, tetapi Hipohamiltonian. Pada graf Petersen diperumum untuk GP_{n,1} adalah tidak Hamiltonian, tetapi Hipohamiltonian. Graf Petersen diperumum GP_{n,2} untuk n ≡ 0(mod 6), 1(mod 6), 2(mod 6), 3 (mod 6), 4(mod 6)bersifat Hamiltonian dan Hipohamiltonian. Sedangkan untuk 5(mod 6) tidak bersifat Hamiltonian tetapi Hipohamiltonian.

ENGLISH:

In graph theory there are several properties of connectedness, that is the characteristics of Hamiltonian and Hypohamiltonian. Hamiltonian graph is cycle through each point exactly once. So that a graph is said to have the properties of the Hamiltonian if the starting point at the end point, through each point exactly once. Hypohamiltonian graph if not the graph is Hamiltonian, but if you removed one point form a Hamiltonian graph. Petersen graph is a cubic graph with 10 points, 15 sides and every point of degree three. Petersen graph generalized is
denoted GP_{n,k}, for positive numbers n and k with 2 ≤ 2k <n. Petersen graph is not Hamiltonian, but Hypohamiltonian. In the generalized Petersen graph for GP_{n,1} is not Hamiltonian, but Hypohamiltonian. Generalized Petersen graph GP_{n,2} for n ≡ 0(mod 6), 1(mod 6), 2(mod 6), 3 (mod 6), 4(mod 6) has characteristics of Hamiltonian and Hypohamiltonian. As for the 5 (mod 6) is not characteristics of Hamiltonian but Hypohamiltonian.

Item Type: Thesis (Undergraduate)
Supervisor: Irawan, Wahyu Hengky and Barizi, Ahmad
Keywords: Petersen; Petersen Diperumum; Hamiltonian; Hipohamiltonian; Petersen; Generalized Petersen
Subjects: 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010105 Group Theory and Generalisations
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Cici Erisa Maulidah
Date Deposited: 29 May 2017 04:20
Last Modified: 29 May 2017 04:20
URI: http://etheses.uin-malang.ac.id/id/eprint/6758

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