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A graph with no isolated vertices is edge critical with respect to total restrained domination if for any non-edge $e$ of $G$, the total restrained domination number of $G+e$ is less than the total restrained domination number of $G$. We call these graphs $\gamma_{tr}$-edge critical. In this paper, we characterize all $\gamma_{tr}$-edge critical unicyclic graphs.
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