Let T be a tournament on n vertices. Prove that:
A question from my book I am not sure how to do, anyone can show me how to solve or any tips on tackling this problem?
Thanks =)
Edit: all my stats were deleted :P
Thanks for the reply.
So the degree has to be n-1 because in a tournament every vertex is connected to every other vertex.
I'm having trouble wraping my head around the concept here... This is what I am understanding, in the tournament, the sum of all out degree must equal the sum of all in degree(intuitively for every out, there must be an in)
Maybe I am misunderstanding the question but what is the signifigance of squaring it? If x=y then of course $\displaystyle x^2=y^2$
$\displaystyle \sum (outdeg(v)^2 - indeg(v)^2)$ Would this not equal zero?
I'm sorry but I really do appreciate the help.
Thanks
Yes.
You are correct, but you will not use this until later.I'm having trouble wraping my head around the concept here... This is what I am understanding, in the tournament, the sum of all out degree must equal the sum of all in degree(intuitively for every out, there must be an in)
This is what you are trying to show$\displaystyle \sum (outdeg(v)^2 - indeg(v)^2)$ Would this not equal zero?
Hint factor.