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anonymous

  • 5 years ago

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!?

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  1. myininaya
    • 5 years ago
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    omg graph theory is cool let me think

  2. myininaya
    • 5 years ago
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    have you ever heard of the degree sequence algorithm

  3. myininaya
    • 5 years ago
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    Write it in decreasing order

  4. anonymous
    • 5 years ago
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    Should be no, since 2 of the vertices are connected to every other vertex. Why is this a contradiction?

  5. myininaya
    • 5 years ago
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    (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

  6. myininaya
    • 5 years ago
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    yes you are correct bond

  7. myininaya
    • 5 years ago
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    (4,3,1,1,0)

  8. myininaya
    • 5 years ago
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    repeat the algorithm

  9. anonymous
    • 5 years ago
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    rings a bell myin, go with that one for the proof, but it's good to understand why

  10. myininaya
    • 5 years ago
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    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

  11. myininaya
    • 5 years ago
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    so there is no simple graph with (5,5,4,2,2,1)

  12. myininaya
    • 5 years ago
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    it is good to understand why, but I never knew why lol i don;t think

  13. anonymous
    • 5 years ago
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    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.

  14. anonymous
    • 5 years ago
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    Do you know if the algorithm always works? I don't remember.

  15. myininaya
    • 5 years ago
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    as long as you dont have mixed graphs

  16. anonymous
    • 5 years ago
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    Also, sorry fort butting in :-[

  17. myininaya
    • 5 years ago
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    why? remember i like your number theory style so i think you are cool

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