I have the following problem that I don't have a clue even how to start, reaching dead ends all the time.
The problem: G=(V,E) is a Planar graph, each face in this graph is hexagon or pentagon. Also, each vertex degree is 3 (deg(v) = 3). I need to prove that on each graph that follows these rules, the number of pentagons is constant and won't be changed.
Any help would be welcomed :)
EDIT: |V| = n
2|E| = 3*|V|=3n --> |E| = 3n\2
I don't have any information about the number of faces I have so I'm reaching dead end here