For a graph $G = (V, E)$, the $γ$-graph of $G$ is the graph whose vertex set is the collection of minimum dominating sets, or $γ$-sets of $G$, and two $γ$-sets are adjacent if they differ by a single vertex and the two different vertices are adjacent in $G$. An open question in $γ$-graphs is whether every bipartite graph is the $γ$-graph of some bipartite graph. We answer this question in the negative by demonstrating that $K_{2, 3}$ is not the $γ$-graph of any bipartite graph.