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Let $k$ be a non-negative integer, $G$ and $G'$ are {\\it $k$-hypomorphic up to complementation} if for every $k$-element subset $K$ of $V$, the induced subgraphs $G\\_{\\restriction K}$ and $G'\\_{\\restriction K}$ are isomorphic up to complementation. 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Two graphs $G$ and $G'$ with vertex set $V$ are {\\it isomorphic up to complementation} if $G'$ is isomorphic to $G$ or to the complement $\\bar G$ of $G$. Let $k$ be a non-negative integer, $G$ and $G'$ are {\\it $k$-hypomorphic up to complementation} if for every $k$-element subset $K$ of $V$, the induced subgraphs $G\\_{\\restriction K}$ and $G'\\_{\\restriction K}$ are isomorphic up to complementation. 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