Embedding of the join of P3 and C4

by Solarmew
Tags: embedding, join
Solarmew is offline
Dec20-12, 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 4-6-1, and C4 is 3-7-2-5, but I don't think that's even relevant.
Any help is appreciated.

Attached Thumbnails
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
Solarmew is offline
Dec21-12, 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