1. The problem statement, all variables and given/known data http://en.wikipedia.org/wiki/Dual_graph I am trying to show that if a graph G is connected, then each face of its dual graph G* contains exactly one vertex of G. 2. Relevant equations 3. The attempt at a solution I tried counting the vertices in G and the faces in G*. I drew enough counterexample to see that if G has two components, then one face contains two vertices of G. My mind just gets tangled when I try to visualize this!