The number of vertex can be calculated from the Hamilton circuits.
The value of N is 6
The variable N is used to always represent the number of vertices.
So, we represent the Hamilton circuits as:
[tex]H = 120[/tex]
The value of N is calculated as follows:
[tex](N - 1)! = H[/tex]
Substitute 120 for H
[tex](N - 1)! = 120[/tex]
Express 120 as a factorial
[tex](N - 1)! = 5![/tex]
Cancel out factorials
[tex]N - 1 = 5[/tex]
Add 1 to both sides
[tex]N = 1 + 5[/tex]
[tex]N = 6[/tex]
Hence, the value of N is 6
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