example of planar graph with two different embeddings into the plane

Consider the following two plane graphs:

The plane graph $G_1$.

The plane graph $G_2$.

Clearly the multigraph associated with each of these plane graphs is the same, but the two plane graphs are not isomorphic: in $G_1$, every face is adjacent to the central region, while in $G_2$ there is no face adjacent to every other. This also implies that their dual graphs are non-isomorphic.

Title	example of planar graph with two different embeddings into the plane
Canonical name	ExampleOfPlanarGraphWithTwoDifferentEmbeddingsIntoThePlane
Date of creation	2013-03-22 14:17:03
Last modified on	2013-03-22 14:17:03
Owner	archibal (4430)
Last modified by	archibal (4430)
Numerical id	5
Author	archibal (4430)
Entry type	Example
Classification	msc 05C10