I have difficulties with the following. We prooved the matrix-tree-theorem, and as I understand it should be useful here, but still...somehow I can't put the details together...the problem is as follows...
Let $G=(V,E)$ be a graph and denote by $t(G)$ the number of different spanning trees of $G$. Furthermore, construct graph $G'$ by replacing one of it's edges by (i) $n$ parallel edges and (ii) by a path of length 2.
Describe $t(G')$ in relation to $t(G)$, $t(G-e)$, and $t(G/e)$ for both situations (i) and (ii). [I guess what is meant here is express $t(G')$ by using $t(G)$, $t(G-e)$, and $t(G/e)$, the last one being the graph $G$ contracted on edge $e$.]
Always so thankful for your help.. :)