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对于无向图的情况，基尔霍夫矩阵为 $K=D-A$，其中 $D$ 为度数矩阵，$A$ 为邻接矩阵。树的个数为去掉 $K$ 一行一列的行列式的值。对于外向树，$D$ 为每个点的入边度数和，内向树相反。此时需要去掉根所在行列。BEST 定理：有向欧拉图的欧拉回路个数为：内向树个数乘以 $\prod\limits_{i=1}^{n}deg_i$，其中 $deg_i$ 为 $i$ 号点的度数。
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点赞过三万更新狗鲸鱼写真集
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