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Math Help - Graph Theory: A has 15 edges, Ā has 13 edges, how many vertices does A have?

  1. #1
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    Exclamation Graph Theory: A has 15 edges, Ā has 13 edges, how many vertices does A have?

    Discrete Math: Graph Theory #54.
    If A is a simple graph with 15 edges, and Ā has 13 edges, how many vertices does A have?

    Can anyone give me the answer and how to arrive at it?

    Thanks a bunch,
    Yvonne
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by yvonnehr View Post
    Discrete Math: Graph Theory #54.
    If A is a simple graph with 15 edges, and Ā has 13 edges, how many vertices does A have?

    Can anyone give me the answer and how to arrive at it?

    Thanks a bunch,
    Yvonne
    do you know this statement?

    Let \overline{G} be the complementary graph of G. Then
    |E(\overline{G})| + |E(G)| = \left({\begin{array}{c} |V(G)| \\ 2 \end{array}}\right)
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    Arrow Equation -> Handshaking Theorem?

    Quote Originally Posted by kalagota View Post
    do you know this statement?

    Let \overline{G} be the complementary graph of G. Then
    |E(\overline{G})| + |E(G)| = \left({\begin{array}{c} |V(G)| \\ 2 \end{array}}\right)
    I don't believe I have seen this. Is this related or some rendition of the Handshaking Theorem?
    -Ivy
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  4. #4
    MHF Contributor kalagota's Avatar
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    i dont think so.. we discussed this as a remark in graph operations..
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    Reading new equation.

    Quote Originally Posted by kalagota View Post
    do you know this statement?

    Let \overline{G} be the complementary graph of G. Then
    |E(\overline{G})| + |E(G)| = \left({\begin{array}{c} |V(G)| \\ 2 \end{array}}\right)
    Tell me I am reading this right.

    The sum of the cardinality of (edges) G and G-compliment equals to the cardinality of (vertices) G.

    Sorry if I am not getting this correctly. It is very late for me. :-) You know how it goes.
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  6. #6
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by yvonnehr View Post
    Tell me I am reading this right.

    The sum of the cardinality of (edges) G and G-compliment equals to the cardinality of (vertices) G.

    Sorry if I am not getting this correctly. It is very late for me. :-) You know how it goes.
    ... cardinality of (vertices) G taken 2..

    EDIT: that is the usual combination formula..
    Last edited by kalagota; June 22nd 2008 at 11:37 PM.
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