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In 1964, Erd\\H{o}s, Hajnal and Moon showed that $sat(n,K_r)=(r-2)n+o(n)$ for $r \\geq 3$, where $sat(n,K_r)$ is the minimum number of edges in a $K_r$-saturated graph on $n$ vertices, and determined the unique extremal graph. This graph has many twins, leading us to define $tsat(n,K_r)$ to be the minimum number of edges in a twin-free $K_r$-saturated graph on $n$ vertices. 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