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If any of the graphs below have a Hamiltonian circuit, list the vertices of the complete circuit. There may be many possibilities. For full credit, just list one for each graph, if the circuit exists

If any of the graphs below have a Hamiltonian circuit list the vertices of the complete circuit There may be many possibilities For full credit just list one fo class=

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sqdancefan

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Answer:

  1. ABHGEFDCA
  2. does not exist
  3. ECBADFE

Step-by-step explanation:

A Hamiltonian circuit visits each node once and returns to its start. There is no simple way to determine if such a circuit exists.

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For graph 2, if there were a circuit, paths ACB, ADB, and AEB would all have to be on it. Inclusion of all of those requires visiting nodes A and B more than once, so the circuit cannot exist.

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For graph 3, the circuit must include paths BAD and DFE. That only leaves node C, which can be reached from both nodes B and E, so path ECB completes the circuit.

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