Fengming Dong, Jun Ge, Zhangdong Ouyang

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.