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A \((p,q)\)-graph is said to be a permutation graph if there exists a bijection function \( f: V(G) \to \{1, 2, \ldots, p\} \) such that the induced edge function \( h_f: E(G) \to \mathbb{N} \) is defined as follows:
\[
h_f(x_i, x_j) =
\begin{cases}
{}^{f(x_i)}P_{f(x_j)}, & \text{if } f(x_j) < f(x_i); \\
{}^{f(x_j)}P_{f(x_i)}, & \text{if } f(x_i) < f(x_j).
\end{cases}
\]
In this paper, we investigate the permutation labelings of wheel-related graphs.