<p>We denote by a <em>triangulation</em> a (simple) maximal planar graph. How many triangulations on <span class="math-container">$n$</span> vertices are there? How many triangulations are there if we cannot distinguish the vertices, i.e. isomorphic triangulations are seen as equal?</p>
<p>All results I can find are for plane graphs, i.e. concrete embeddings, and not abstract graphs.</p>

CC BY-SA 4.0
2020-12-01T07:13:34.380Z
I might be mistaken here but i thought maximal planar graphs have unique embeddings, so counting (non isomorphic) plane triangulations should be the same?
daniello
CC BY-SA 4.0
2020-12-04T02:40:39.040Z
This question may be more suitable for math.stackexchange.
Kai
<graph-theory><co.combinatorics><planar-graphs><computational-geometry><delaunay-triangulation>
How many maximal planar graphs are there?
John S
# How many maximal planar graphs are there?

(Asked by: username_0 on 2020-12-01)

We denote by a *triangulation* a (simple) maximal planar graph. How many triangulations on $n$ vertices are there? How many triangulations are there if we cannot distinguish the vertices, i.e. isomorphic triangulations are seen as equal?

All results I can find are for plane graphs, i.e. concrete embeddings, and not abstract graphs.

**Tags:** graph-theory, co.combinatorics, planar-graphs, computational-geometry, delaunay-triangulation

> **Comments:**
> **username_1**: I might be mistaken here but i thought maximal planar graphs have unique embeddings, so counting (non isomorphic) plane triangulations should be the same?  
> **username_2**: This question may be more suitable for math.stackexchange.  

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