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For a graph $G$, the $\gamma$-graph of $G$, $G(\gamma)$, is the graph whosevertices correspond to the minimum dominating sets of $G$, and where twovertices of $G(\gamma)$ are adjacent if and only if their correspondingdominating sets in $G$ differ by exactly two adjacent vertices. In this paper,we present several variations of the $\gamma$-graph including those usingidentifying codes, locating-domination, total-domination, paired-domination,and the upper-domination number. For each, we show that for any graph $H$,there exist infinitely many graphs whose $\gamma$-graph variant is isomorphicto $H$.

A note on some variations of the $\gamma$-graph