Embeddings of Graphs in a Torus and in a Moebius Strip

This Demonstration illustrates the fact that any graph of genus 1 can be embedded in a torus and any graph of non-orientable genus 1 can be embedded in a Möbius strip. All the graphs in this Demonstration can be embedded in both surfaces. To move the graph vertices, drag the colored points on the planar diagram. The path connecting the points is chosen based on the distance between the points.