Consider a connected graph in which every vertex has degree 7. Let v b the number of vertices in the graph.

a. Suppose v = 10. How many edges does the graph have, explain why?

b. All vertices have degree 7. Which of the following number of vertices are possible, explain why? 6 8 9 103

c. Let v = 10. Prove the the graph is not planar. Write the proof in words, making clear the style of proof you are using.