1. The problem statement, all variables and given/known data Take an n-cycle and connect two of its nodes at distance 2 by an edge. Find the number of spanning trees in this graph. 2. Relevant equations n^(n-2)? 3. The attempt at a solution I honestly have no idea on how to start this problem. I know the definition of an n-cycle. My approach towards problems like this would be to construct a graph. For example a cube is a 4-cycle with nodes 1,2,3,4. then connect nodes 1 and 3 which gives the distance of 2. This graph has 8 spanning trees. I counted them. But I have no idea what the general formula is for this. Any input would be much appreciated!