Express the number of spanning trees in term of degrees

Abstract

It is well-known that the number of spanning trees, denoted by $\ddot{I}„(G)$, in a connected multi-graph $G$ can be calculated by the Matrix-Tree theorem and Tutte's deletion-contraction theorem. In this short note, we find an alternate method to compute $\ddot{I}„(G)$ by degrees of vertices.

9 pages, 2 figures