The number of Hamilton Circuits with 8 vertices are 5040.
Given that, a complete, weighted graph with 8 vertices.
<h3>What are Hamilton Circuits?</h3>
A Hamiltonian circuit is a circuit that visits every vertex once with no repeats. Being a circuit, it must start and end at the same vertex. A Hamiltonian path also visits every vertex once with no repeats, but does not have to start and end at the same vertex.
For N vertices in a complete graph, there will be (n−1)!=(n−1)(n−2)(n−3)…3⋅2⋅1 routes. Half of these are duplicates in reverse order, so there are (n−1)!/2 unique circuits.
A complete graph with 8 vertices would have = 5040 possible Hamiltonian circuits. Half of the circuits are duplicates of other circuits but in reverse order, leaving 2520 unique routes.
Therefore, the number of Hamilton Circuits with 8 vertices are 5040.
Learn more about the Hamilton Circuits here:
brainly.com/question/24725745.
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