Question: If you stick a vertex in the middle of an (n - 1)-vertex cycle Cn-1 (where n is at least three) and connect it to all vertices on the cycle, you obtain the wheel graph, denoted Wn. (It has that extra vertex, see.) A few wheels are shown in Figure - Wheels. (Note that W4 is also K4 but differently drawn than in Figure - complete graph). Let n ≥ 4. Find and prove a formula for the number of edges of the wheel Wn.
