Proving that finding wheel subgraphs is NP-complete Can you help me with this problem ?


  Given an undirected graph $G$ and an integer $n$, prove that determining whether the graph has wheel on $n$ vertices $W_{n}$ (a wheel $W_{i}$ is such that $i$ nodes form a cycle and a $i+1$st node is connected to all other nodes, resulting in $2i$ edges) is NP-complete.
Hint: Hamiltonian Cycle is $NP$-Complete.