Question

Is it possible for wheel $W_n$ ($n \ge 3$) to be bipartite?

• A. No
• B. Yes
• C. Do not say
• D. None of these

Hint:

Bipartite graphs have no odd cycles. $W_n$ contains triangles for $n\ge3$.

Answer 1

The Correct Option is A

Step 1: Wheel $W_n$ has a central vertex connected to all vertices of a cycle $C_{n-1}$.}
Step 2: For $n \ge 3$, the cycle $C_{n-1}$ is odd when $n-1$ is odd, i.e., $n$ even. But the central vertex creates odd cycles. So $W_n$ is not bipartite for any $n\ge3$.}