# 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 ExampleOfPlanarGraphWithTwoDifferentEmbeddingsIntoThePlane 2013-03-22 14:17:03 2013-03-22 14:17:03 archibal (4430) archibal (4430) 5 archibal (4430) Example msc 05C10