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Joystar1977
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- Jul 24, 2013
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Consider the complete graph with 5 vertices, denoted by K5.
E.) Does K5 contain Hamiltonian circuits? If yes, draw them.
I know that a Hamiltonian circuit is a graph cycle through a graph that visits each node exactly once. However, the trivial graph on a single node is considered to possess a Hamiltonian cycle, but the connected graph on two nodes is not. A graph possessing a Hamiltonian circuit is said to be a Hamiltonian graph.
Is it correct that K5 doesn't contain Hamiltonian circuits because this is a connected graph on two nodes?
E.) Does K5 contain Hamiltonian circuits? If yes, draw them.
I know that a Hamiltonian circuit is a graph cycle through a graph that visits each node exactly once. However, the trivial graph on a single node is considered to possess a Hamiltonian cycle, but the connected graph on two nodes is not. A graph possessing a Hamiltonian circuit is said to be a Hamiltonian graph.
Is it correct that K5 doesn't contain Hamiltonian circuits because this is a connected graph on two nodes?