大部分见到的定时是这样的： set $N_n = {1, 2, \cdots , n}$ if $n$ is a positive integer and The Bubble-sort Graph $B_n$, is a graph with vertex set that consist of all $n!$ permutations on $N_n$. The vertex set $V(B_n) = {x_1,\cdots, x_n | x_i \in N_n$ and $x_i \neq x_j$ for $i \neq j}$. The adjacency is defined as follows: $x_1\cdots x_{i-1}x_i \cdots x_n$ is adjacent to $y_1\cdots y_{i-1}y_i \cdots y_n$ through an edge of dimension $i$ with $2 \leq i \leq n$ if $y_j = x_j$ for every $j \in N_n-{i-1, i}, y_{i-1} = x_i$, and $y_i = x_{i-1}$, i.e., swap $x_{i-1}$ and $x_i$.
那么，递归的定义是什么？就是比如说如何有3维的图构造4维的图
不知道你这个问题是否已经解决, 如果还没有解决的话: