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Express the number of spanning trees in term of degrees
Applied Mathematics and Computation  (IF4.091),  Pub Date : 2021-10-10, DOI: 10.1016/j.amc.2021.126697
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.