A graph is said to be cordial if it has a 0-1 labeling that satisfies certain properties. A wheel \(W_n\) is the graph obtained from the join of the cycle \(C_n\) (\(n \geq 3\)) and the null graph \(N_1\). In this paper, we investigate the cordiality of the join and the union of pairs of wheels and graphs consisting of a wheel and a path or a cycle.