It is well-known that the number of spanning trees, denoted by $\tau \left(G\right)$, in a connected multi-graph $G$ can be calculated by the Matrix-Tree Theorem and Tutte’s deletion-contraction formula. In this short note, we find an alternate method to compute $\tau \left(G\right)$ by degrees of vertices.

中文翻译：

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用度数表示生成树的数量

众所周知，生成树的数量表示为 $\tau \left(G\right)$, 在一个连通的多重图中 $G$可以通过矩阵树定理和 Tutte 的删除收缩公式计算。在这个简短的说明中，我们找到了一种替代方法来计算$\tau \left(G\right)$ 按顶点的度数。