Is there a straightforward way to count the number of spanning trees of a graph which are all rooted at the same point. Sources on the subject, if possible, would be much appreciated.
In case it helps, I'm specifically working with the the standard nearest neighbour graph on $\mathbb{Z}^2 \bigcap [0,n] ^2 $, and I would like to count the spanning trees rooted at $(0,0)$.
If you are talking about undirected graph, then I guess number of spanning trees is same whether it is rooted or not. In that case, https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem , kirchoff's theorem can help count them.
If you are talking about directed rooted trees, then you might want to look for kirchoffs theorem for directed multi graph.
Correct me if I am wrong..