# HAMILTONIAN AND HYPOHAMILTONIAN OF GENERALIZED PETERSEN GRAPH GPn,6

## DOI:

https://doi.org/10.31258/jomso.v1i2.18## Keywords:

Petersen graph, generalized Petersen graph, Hamiltonian, Hypohamiltonian## Abstract

*This article discusses the Hamiltonian and **H**ypo**h**amiltonian properties of **G**eneralized Petersen** G**raphs GP _{n,6}. *

*A Hamiltonian graph is a graph that has a Hamiltonian cycle. So, a graph is called to be Hamiltonian and has a cycle that passes through each vertex exactly once. A Hypohamiltonian graph is if it is not a Hamiltonian graph, but if one vertex is removed it will be Hamiltonian. The Petersen graph is a cubic graph with ten vertices and fifteen edges and each vertex is of degree three. The generalized Petersen graph is denoted GP*

_{n,k}*, for positive numbers n and k with 2 ≤ 2k <*

*????. The Petersen graph is not a Hamiltonian graph, but is Hypohamiltonian. In the Generalized Petersen graph for GP*

_{n,6}*for n ≡ 1(mod 13), n ≡ 3(mod 13), n ≡ 7(mod 13), n ≡ 9(mod 13) is a Hamiltonian, for n ≡ 0(mod 13) is a hypohamiltonian, and for n ≡ 2(mod 13), n ≡ 4(mod 13), n ≡ 5(mod 13), n ≡ 6(mod 13), n ≡ 8(mod 13) neither.*

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