Two questions I'm stuck with:
If C is a cycle, and e is an edge connecting two nonadjacent nodes of C, then we call e a chord of C. Prove that if every node of a graph G has degree at least 3, then G contains a cycle with a chord.
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.
Thanks....