Journal of Combinatorial Theory Series B
The number of splanning trees in a finite graph is first expressed as the derivative (at 1) of a determinant and then in terms of a zeta function. This generalizes a result of Hashimoto to non-regular graphs.
Northshield, S. (1998). A note on the Zeta Function of a Graph. Journal of Combinatorial Theory Series B, 74, 408-410.