Which of the following is $\textbf{not}$ TRUE?

(a) In a complete graph $K_n$ ($n$ $\geq$ $3$), Hamiltonian cycle exists for all n.

(b) In a complete bipartite graph $K_{m,n}$ (m $\geq$ 2 and n $\geq$2), Hamiltonian cycle exists $\Leftrightarrow$ $m$ $=$ $n$.

(C) In a cycle graph $C_n$($n \geq$3), Hamiltonian cycle exits for all $n$

(d) In a wheel graph $W_n$ ($n \geq 4$), Hamiltonian cycle exits $\Leftrightarrow$ $n$ is even.