I've been having trouble wrapping my head around this concept. How do I calculate the degree of a face in planar graphs. In our textbook, we are given this image:
where $f_1, f_2, f_3, f_4$ are the faces.
In the textbook, it gives the degrees of the four faces as $$deg(f_1) = 6$$ $$deg(f_2) = 3$$ $$deg(f_3) = 5$$ $$deg(f_4) = 14$$
I don't understand how they got 6 for $f_1$ and 14 for $f_4$. I know this is a very simple question, but I'm just not getting it for some reason. I would appreciate the help.
Thanks
Think of the edges as being two sided. As you move around the face of $f_1$ you see both sides of the leaf edge, so that edge is counted twice. Likewise, when you travel around the outer face you see the bridge edge twice (both sides of it) so it is counted twice. Hope this helps.