
#1
Dec2012, 11:20 PM

P: 36

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 461, and C4 is 3725, but I don't think that's even relevant. Any help is appreciated. 



#2
Dec2112, 03:41 PM

P: 36

nm, i got it...



Register to reply 
Related Discussions  
Embedding Sn into An+1  Linear & Abstract Algebra  3  
RP2 into R4 embedding  Differential Geometry  1  
embedding dimension  General Physics  0  
RP2 into R4 embedding  Calculus & Beyond Homework  0  
C is a circle embedded smoothly in R4, show that . . .  Set Theory, Logic, Probability, Statistics  0 