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Section4.4Drawing Graphs on Other surfaces

We saw, using stereographic projection, that being able to draw a graph on the sphere is the same as being able to draw the graph on the plane. In this section we will discuss drawing graphs on other surfaces -- the torus and the Mobius band we will discuss in detail, though similar ideas work for any surface. We need a way to represent such graphs on a piece of paper, for use in a book (or on the exam, say). Much of the material from the rest of this chapter (Kuratowski's theorem, Euler's theorem) have analogues for other surfaces, but are beyond the scope of this module.

Figure4.4.1\(K_5\) and \(K_{3,3}\) drawn on a torus