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For a graph $G = (V, E)$, the $\gamma$-graph of $G$ is the graph whose vertexset is the collection of minimum dominating sets, or $\gamma$-sets of $G$, andtwo $\gamma$-sets are adjacent if they differ by a single vertex and the twodifferent vertices are adjacent in $G$. An open question in $\gamma$-graphs iswhether every bipartite graph is the $\gamma$-graph of some bipartite graph. Weanswer this question in the negative by demonstrating that $K_{2, 3}$ is notthe $\gamma$-graph of any bipartite graph.

A Bipartite Graph That Is Not the $\gamma$-Graph of a Bipartite Graph