Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Embedding of the join of P3 and C4

  1. Dec 20, 2012 #1
    Given a join of P3 and C4, "Adjust the picture if necessary so that at most two edges cross in any point (not representing a vertex). Then erect an overpass at every point where two edges of G cross. The genus of G, is the minimum number of overpasses that must be added to the plane so that G can be embedded in the resulting surface."
    The objective is to prove that the graph of the join has genus=1, so it can be embedded on a torus. But I can't figure out how to rearrange the vertices in such a way :( I'm assuming there supposed to be only one point of intersection, but the best I can do is three...
    Here P3 is 4-6-1, and C4 is 3-7-2-5, but I don't think that's even relevant.
    Any help is appreciated.

    attachment.php?attachmentid=54139&stc=1&d=1356066965.png
     

    Attached Files:

  2. jcsd
  3. Dec 21, 2012 #2
    nm, i got it...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Embedding of the join of P3 and C4
  1. Manfold embeddings (Replies: 19)

Loading...