Having a bit of trouble with this question:
Suppose G is a 4-regular connected graph with a planar embedding such that every face has degree 3 or 4, and further that any 2 adjacent faces have different degrees.
For the first part, I have to prove that G has no bridges and hence that every edge in G is on the boundary of 2 distinct faces.
For the second part, I must determine precisely the number of vertices, edges, faces of degree 3, and faces of degree 4 in G.
Something tells me to use Euler's formula for the second part but I'm quite confused at the first part.
Any help would be greatly appreciated!