Question

Find the number of edges of the wheel graph $W_n$.

• A. \(n - 1\)
• B. \(\dfrac{n(n - 1)}{2}\)
• C. \(2n\)
• D. \(n \times 2^{n - 1}\)

Hint:

Wheel graphs combine a cycle and a star structure, doubling the edge count relative to the cycle length.

Answer 1

The Correct Option is C

The wheel graph \(W_n\) consists of a cycle of \(n\) vertices plus one central vertex connected to all \(n\) outer vertices. The cycle has \(n\) edges and the central connections add another \(n\), so total: \[ n + n = 2n \text{ edges} \]