The general position number ${\rm gp}(G)$ of a graph $G$ is the cardinality of a largest set of vertices $S$ such that no element of $S$ lies on a geodesic between two other elements of $S$. The complementary prism $G\overline{G}$ of $G$ is the graph formed from the disjoint union of $G$ and its complement $\overline{G}$ by adding the edges of a perfect matching between them. It is proved that ${\rm gp}(G\overline{G})\le n(G) + 1$ if $G$ is connected and ${\rm gp}(G\overline{G})\le n(G)$ if $G$ is disconnected. Graphs $G$ for which ${\rm gp}(G\overline{G}) = n(G) + 1$ holds, provided that both $G$ and $\overline{G}$ are connected, are characterized. A sharp lower bound on ${\rm gp}(G\overline{G})$ is proved. If $G$ is a connected bipartite graph or a split graph then ${\rm gp}(G\overline{G})\in \{n(G), n(G)+1\}$. Connected bipartite graphs and block graphs for which ${\rm gp}(G\overline{G})=n(G)+1$ holds are characterized. A family of block graphs is constructed in which the ${\rm gp}$-number of their complementary prisms is arbitrary smaller than their order.

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关于互补棱镜的一般位置数

图 $G$ 的一般位置数 ${\rm gp}(G)$ 是最大顶点集 $S$ 的基数，这样 $S$ 的任何元素都不会位于 $ 的其他两个元素之间的测地线上新元。$G$ 的互补棱镜$G\overline{G}$ 是$G$ 和它的补集$\overline{G}$ 的不相交并集通过添加它们之间完美匹配的边形成的图。证明 ${\rm gp}(G\overline{G})\le n(G) + 1$ 如果 $G$ 连通且 ${\rm gp}(G\overline{G})\le如果 $G$ 断开连接，则为 n(G)$。${\rm gp}(G\overline{G}) = n(G) + 1$ 成立的图 $G$，假设 $G$ 和 $\overline{G}$ 是连通的，则被表征。证明了 ${\rm gp}(G\overline{G})$ 的急剧下界。如果 $G$ 是连通二部图或分裂图，则 ${\rm gp}(G\overline{G})\in \{n(G), n(G)+1\}$。表征了 ${\rm gp}(G\overline{G})=n(G)+1$ 成立的连通二部图和块图。构建了一个方块图族，其中它们互补棱镜的 ${\rm gp}$-number 任意小于它们的阶数。