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Math Help - Graph problem

  1. #1
    Junior Member
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    Graph problem

    Hi again.

    I've got a question about :

    1.
    Can there be a collection of 4 persons in which every person has exactly two friends?
    2.
    Can there be a collection of 6 persons in which every person has exactly three friends?
    3 .
    How about a collection of 7 persons in which every person has exactly three friends?

    For each case draw the friendship graph if such setting is possible, or prove it is impossible.?

    Thank you for any help
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  2. #2
    MHF Contributor

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    Quote Originally Posted by Snowboarder View Post
    1. Can there be a collection of 4 persons in which every person has exactly two friends?

    3 .How about a collection of 7 persons in which every person has exactly three friends?
    For #1 think about a rectangle.

    For #3. Is it possible for a graph to have seven odd vertices?
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