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Math Help - Planar graph

  1. #1
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    Planar graph

    Hi
    I have this graph
    Planar graph-drawing1-2-.jpg
    now i should check if this graph can be planar.

    v - number of vertices
    e - number of edges
    f - number of faces

    So it's hold the theorem "If v ≥ 3 then e 3v − 6 "
    v = 9, e = 15
    15 ≤ 21

    and should hold v - e + f = 2 from here f = 2 - v + e = 2 - 9 + 15 = 8
    so f = 8 now my question is how to easily count faces (regions bounded by edges, including the outer, infinitely large region) of the graph??
    thanks
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  2. #2
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    Re: Planar graph

    You need the graph to be embedded in the plane (that is, drawn with no edges crossing) to have faces defined. Also, I think your graph is not planar. The condition you are using works like this "If the graph is planar, then e \leq 3v - 6" but the latter doesn't prove the first, that is "If e \leq 3v - 6, then the graph is planar" is WRONG.
    Last edited by Vlasev; August 21st 2012 at 01:06 AM.
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