Exercise 15.

Explain why we cannot use the same sort of proof we did in Exercise 4.3.14 to prove that the graph below is not planar. Then explain how you know the graph is not planar anyway.

A graph with 11 vertices. A single vertex in the center, then five vertices equally spaced around a ring around it, and five more equally spaced around a ring around those. Edges form the sides of a pentagon for the outer ring of vertices and also the inner ring of vertices. Each outer vertex is also adjacent to two inner vertices: the two on either side of the vertex closest to it. Finally, every inner vertex is also adjacent to the center vertex.
Hint.
in-context