The Jacob Snark

This graph is 10 points, shaped in 2 pentagons. The idea for this graph came from one of the named graphs on the handout, the Peterson Graph. I just changed it a bit and added more.

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Questions:

1. How many colors minimum can you use to color all edges so that no adjacent edges are the same color?

2. This graph is not planar. How many edges must be removed to make it planar? Remove that edge, and show its planarity on the computer.

3. Does an Eulerian trail exist? Why or why not?

Jacob Snyder, Created with GeoGebra