Let S be a non-empty finite set. A flag of S is a set f of non-empty proper subsets of S such that $X\subseteq Y$ or $Y\subseteq X$ for all $X,Y\in f$. The set $\{|X|:X\in f\}$ is called the type of f. Two flags f and $f^{\prime }$ are in general position with respect to S if $X\cap Y=\varnothing$ or $X\cup Y=S$ for all $X\in f$ and $Y\in f^{\prime }$. For a fixed type T, Klaus Metsch defined the general position graph $\mathrm{\Gamma }(S,T)$ whose vertices are the flags of S of type T with two vertices being adjacent when the corresponding flags are in general position. In this paper, we characterize the full automorphism groups of $\mathrm{\Gamma }(S,T)$ in the case that $|T|=2$. In particular, we solve an open problem proposed by Klaus Metsch.

设S为非空有限集。S的标志是S的非空真子集的集合f，使得$X\subseteq 是$或者$是\subseteq X$对全部$X,是\epsilon F$。套装$\{|X|：X\epsilon F\}$称为f的类型。两个标志f和$F^{\prime }$相对于S处于一般位置，如果$X\cap 是=\varnothing$或者$X\cup 是=S$对全部$X\epsilon F$和$是\epsilon F^{\prime }$。对于固定类型T，Klaus Metsch 定义了一般位置图$\mathrm{\gamma }（S,\mathrm{时间}）$其顶点是类型T的S的标志，当对应的标志处于一般位置时，两个顶点相邻。在本文中，我们描述了完全自同构群$\mathrm{\gamma }（S,\mathrm{时间}）$在这种情况下$|\mathrm{时间}|=2$。特别是，我们解决了 Klaus Metsch 提出的一个开放问题。