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The connected domination number of $G$, $\\gamma_c(G)$, is the minimum cardinality of a connected dominating set of $G$. A graph $G$ is said to be $k$-$\\gamma_{c}$-critical if the connected domination number $\\gamma_{c}(G)$ is equal to $k$ and $\\gamma_{c}(G + uv) < k$ for every pair of non-adjacent vertices $u$ and $v$ of $G$. 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