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Thread: More trees ....This one is doing my head in ...

  1. #1
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    More trees ....This one is doing my head in ...

    Let T be a tree on 12 vertices which has exactly 3 vertices of degree 3 and exactly onevertex of degree
    2.
    (a) What is the sum of the degrees of the 8 remaining vertices?
    (b) What is the maximum degree of this tree? Justify your answer.
    (c) What is the degree sequence of T?
    (d) Find two non-isomorphic trees with this degree sequence


    Ok everytime I draw a Tree it has 11 vertices only matching the first part of the problem....

    (a) If I could draw the tree would I just add the remaining 8 degrees ie what ever isnt included with the 3 vertices and 3 degrees as well as the degree 2 that is on one vertex.
    (b) Maximum degree ...hmmm would help if i knew what it looked like
    (c) The sequence would just be the degrees ...in a sequence..
    (d) so isomorphic graphs are bijective and share the same vertices being adjacent in a sequence ..therefore I'd have to draw a tree with the sequence but not bijective...

    Any help would be appreciated....when I was a kid looking at my christmas tree, xmas eve hoping for some presents the next morning I never thought I'd do graph theory as an adult..just what goodies I was hoping to get...a good math brain would have been a nice present...thanks Santa ...facepalm..
    Last edited by bee77; Sep 7th 2017 at 05:50 AM.
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  2. #2
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    Re: More trees ....This one is doing my head in ...

    A tree (with at least 2 vertices) must have at least 2 vertices of degree 1. That will help.
    Last edited by Mezza; Sep 7th 2017 at 07:29 AM.
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  3. #3
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    Re: More trees ....This one is doing my head in ...

    Quote Originally Posted by bee77 View Post
    Let T be a tree on 12 vertices which has exactly 3 vertices of degree 3
    and exactly one vertex of degree 2.
    (a) What is the sum of the degrees of the 8 remaining vertices?
    (b) What is the maximum degree of this tree? Justify your answer.
    (c) What is the degree sequence of T?
    (d) Find two non-isomorphic trees with this degree sequence
    More trees ....This one is doing my head in ...-tree.gif
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    Re: More trees ....This one is doing my head in ...

    Thanks plato ,my tree looked like an arrow head ,cheers
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    Re: More trees ....This one is doing my head in ...

    Quote Originally Posted by bee77 View Post
    Thanks plato ,my tree looked like an arrow head ,cheers
    Please post your graph. What do you mean "arrow head".
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  6. #6
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    Re: More trees ....This one is doing my head in ...

    Hey plato,
    I'm in a lecture atm I'll put it up this afternoon (midday )here in aus ...thanx..like a tree from top 3 edges like an arrow then cascades downwards
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  7. #7
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    Re: More trees ....This one is doing my head in ...

    So plato I took a while to respond been tied up with assignments and all other things ...my graph was basically / \
    /\ /\ d oesn't matter I totally stuffed it up
    /\
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