# Combinatorics/Graph QuestionWatch

Thread starter 7 years ago
#1
Given four nodes, how many ways are there to connect all four of them using exactly three edges? Just by writing them all out, I arrived at 16. I'm almost certain this is correct, but I can't think of a way to justify it formally.
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7 years ago
#2
(Original post by Dragon)
Given four nodes, how many ways are there to connect all four of them using exactly three edges? Just by writing them all out, I arrived at 16. I'm almost certain this is correct, but I can't think of a way to justify it formally.
Well if you've written them all out, you should be able to see that there are only two basic shapes.
A continuous line (12 of) and a star formation (4 of). See if you can justify the number of each.
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Thread starter 7 years ago
#3
(Original post by ghostwalker)
Well if you've written them all out, you should be able to see that there are only two basic shapes.
A continuous line (12 of) and a star formation (4 of). See if you can justify the number of each.
Yes, that's great, thanks!
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