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It is known that an \(\alpha\)-labeling of a bipartite graph \(G\) with \(n\) edges can be used to obtain a cyclic \(G\)-decomposition of \(K_{2nx+1}\) for every positive integer \(x\). It is also known that if two graphs \(G\) and \(H\) admit a free \(a\)-labeling, then their vertex-disjoint union also admits a free \(\alpha\)-labeling. We show that if \(G\) is a bipartite prism, a bipartite Möbius ladder, or a connected cubic bipartite graph of order at most 14, then \(G\) admits a free \(a\)-labeling. We conjecture that every bipartite cubic graph admits a free \(\alpha\)-labeling.