Chapter 6.2, Problem 24MS

A torus graph (ExH). The Euler Characteristic $\text{V - E+ F}$ can be applied to other surfaces besides spheres. We can compute it for tori, two-holed ton, and yet more complicated figures; however, for those surfaces the 2 in $\text{V - E + F = 2}$ is replaced by other numbers. Draw a connected graph on a torus that both circles Graph must go around the hole and goes through the hole of the tows. both ways, as marked. Compute $\text{V - E+ F}$ for the graph. Try several other different graphs that go around the torus both ways and again cornpute $\text{V - E+ F}$.