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Math Help - set complements....

  1. #1
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    set complements....

    Hi, having big trouble with this one:

    The
    complement of a graph Z= (V,F) is the graph Z(bar)with
    vertex set Q
    in which there is an edge between two vertices

    x, y elements of
    Qif and only if there is no edge between x and y in Z.
    Suppose that the graph Z
    = (V,F) is self-complementary i.e.

    Z
    and Z(bar)are isomorphic.

    1. Find a formula for
    |F| in terms of n = |Q|.

    2. Prove that Z
    is connected.



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  2. #2
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    Quote Originally Posted by dannyshox View Post
    Hi, having big trouble with this one:

    The
    complement of a graph Z= (V,F) is the graph Z(bar)with
    vertex set Q
    in which there is an edge between two vertices

    x, y elements of
    Qif and only if there is no edge between x and y in Z.
    Suppose that the graph Z
    = (V,F) is self-complementary i.e.

    Z
    and Z(bar)are isomorphic.

    1. Find a formula for
    |F| in terms of n = |Q|.

    2. Prove that Z
    is connected.



    If |F| is the number of edges in graph \mathcal{Z} of ordered n then the number of edges in the complement \overline{\mathcal{Z}} is |Q|=n-|F|.

    This is a standard theorem: At least one of \mathcal{Z} or \overline{\mathcal{Z}} is connected.
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