A graph puzzle ${\rm Puz}(G)$ of a graph $G$ is defined as follows. A configuration of ${\rm Puz}(G)$ is a bijection from the set of vertices of a board graph to the set of vertices of a pebble graph, both graphs being isomorphic to some input graph $G$. A move of pebbles is defined as exchanging two pebbles which are adjacent on both a board graph and a pebble graph. For a pair of configurations $f$ and $g$, we say that $f$ is equivalent to $g$ if $f$ can be transformed into $g$ by a finite sequence of moves. Let ${\rm Aut}(G)$ be the automorphism group of $G$, and let ${\rm 1}_G$ be the unit element of ${\rm Aut}(G)$. The pebble exchange group of $G$, denoted by ${\rm Peb}(G)$, is defined as the set of all automorphisms $f$ of $G$ such that ${\rm 1}_G$ and $f$ are equivalent to each other. In this paper, some basic properties of ${\rm Peb}(G)$ are studied. Among other results, it is shown that for any connected graph $G$, all automorphisms of $G$ are contained in ${\rm Peb}(G^2)$, where $G^2$ is a square graph of $G$.

翻译：拼图拼图 $ rm Puz} (G) 。 拼图 $ $ g$ 定义如下 。 对于一对组合 $f 和 $g$, 我们说 $f$ 相当于$g$, 如果一张棋子图的顶点可以按一定的动作顺序转换成$g$。 请将$@ gut} (G) 的两张图与某个输入图 $G$ 。 棋子的移动的定义是, 交换一个棋盘图 和 泡泡图 $ 。 对于一对组合 $f 美元和 $ g$, 我们说 美元等于 $ g$ 的组合, 如果用一定的动作顺序将美元转换成$g$。 请将$@ gut_ g} (G) 美元作为某个输入G$, 让$% 1 g$ (G) 的单位是美元 。 平面图中的任何一美元是 美元 。