anonymous
  • anonymous
Does there exist a simple graph with 6 vertices of degree 1,2,2,4,5,5? if not, why? and if there is how do I draw it!?
Mathematics
chestercat
  • chestercat
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myininaya
  • myininaya
omg graph theory is cool let me think
myininaya
  • myininaya
have you ever heard of the degree sequence algorithm
myininaya
  • myininaya
Write it in decreasing order

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anonymous
  • anonymous
Should be no, since 2 of the vertices are connected to every other vertex. Why is this a contradiction?
myininaya
  • myininaya
(5,5,4,2,2,1) since 5 is the first number, the algorithm says to remove it and take 1 away from the 5 numbers after
myininaya
  • myininaya
yes you are correct bond
myininaya
  • myininaya
(4,3,1,1,0)
myininaya
  • myininaya
repeat the algorithm
anonymous
  • anonymous
rings a bell myin, go with that one for the proof, but it's good to understand why
myininaya
  • myininaya
4 is the first number now take 1 away from the four numbers after is and you get (2,0,0,-1) but you cant have a vertice with degree 1
myininaya
  • myininaya
so there is no simple graph with (5,5,4,2,2,1)
myininaya
  • myininaya
it is good to understand why, but I never knew why lol i don;t think
anonymous
  • anonymous
I just meant for this problem which has a simple contradiction, I don't think I could do it if it got any more complex.
anonymous
  • anonymous
Do you know if the algorithm always works? I don't remember.
myininaya
  • myininaya
as long as you dont have mixed graphs
anonymous
  • anonymous
Also, sorry fort butting in :-[
myininaya
  • myininaya
why? remember i like your number theory style so i think you are cool

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