Question

Suppose you have a complete, weighted graph with 8 vertices. How many Hamilton Circuits are there in this graph?

Answer 1

The number of Hamilton Circuits with 8 vertices are 5040.

Given that, a complete, weighted graph with 8 vertices.

What are Hamilton Circuits?

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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