# Uniform planar graphs?

What's the name of a planar graph in which every (inner) face has the same number $k$ of vertices? Something like $k$-uniform planar graph?

And is there a name for planar graphs in which every face has at most $k$ vertices?

-
Thanks, Kuba, I looked for such a tag but didn't find it. – Hans Stricker Aug 23 '12 at 8:30

## 1 Answer

If $k=3$ you call the graph a triangulation. If $k=4$ it is called quadrangulation. I am not aware of any other terms for a fixed $k>4$.

For a non-fixed $k$ you might say graphs with face-degree $k$. Or duals of $k$-regular graphs. How about $k$-gonalization?

-
Is it still called a triangulation if the outside face isn't a triangle? – Gerry Myerson Aug 23 '12 at 12:37
@GerryMyerson: Well this depends. If you are coming lets say from the graph drawing or meshing community then you would probably still call it a triangulation. On the other hand, if your background is more on polytopes and graph theory then rather not. – A.Schulz Aug 23 '12 at 12:42