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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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