One of the branches of mathematics that studies the properties of graphs is graph theory. The purpose of this study is to find out how to prove the Hamiltonian on a 5-connected graph. Through the stages, including modeling a complete graph, as well as modeling a 5-connected graph using vertices and cut edges, it was found that is a graph that satisfies the characteristics of a 5-connected graph. Analysis of Hamiltonian on 5-connected graph that 5-connected graph is Hamilton's invention, but it is not uniquely Hamiltonian because it has more than one Hamiltonian circuit.
Keywords: k-connected graph, Hamiltonian, vertex cuts
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