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Math Help - how many vertices does this graph have.....

  1. #1
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    how many vertices does this graph have.....

    Hello,
    plz try to solve this question.

    QUESTION:
    Suppose that a connected planer simple graph has 25 edges. If a plane drawing of this graph has 10 faces, how many vertices does this graph have?
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  2. #2
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    Quote Originally Posted by m777 View Post
    Hello,
    plz try to solve this question.

    QUESTION:
    Suppose that a connected planer simple graph has 25 edges. If a plane drawing of this graph has 10 faces, how many vertices does this graph have?
    Such a graph satisfies Euler's Polyhedron formula:

    n-m+f=2

    where n is the number of vertices, m the number of edges, and f the
    number of faces. So:

    n=2+25-10=17.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Such a graph satisfies Euler's Polyhedron formula:

    n-m+f=2

    where n is the number of vertices, m the number of edges, and f the
    number of faces. So:

    n=2+25-10=17.

    RonL
    Is this just pretty much the same as Euler's Relationship:

    R + N = A + 2 ?
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  4. #4
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    Quote Originally Posted by anthmoo View Post
    Is this just pretty much the same as Euler's Relationship:

    R + N = A + 2 ?
    I am not sure what you are saying but there is:
    1)Euler Formula for Planar Graphs.
    2)Euler Formula for Polyhedra.
    These two formulas are the same.
    #1 is stronger than #2.
    Because I believe one way of proving #2 is from #1.
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    Such a graph satisfies Euler's Polyhedron formula:

    n-m+f=2

    where n is the number of vertices, m the number of edges, and f the
    number of faces. So:

    n=2+25-10=17.

    RonL
    is there a way of finding the number of faces (or regions as its called in our classnotes) from just looking at a graph? eg. how many faces/regions does K_{3,3} have?
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