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[parent] example of planar graph with two different embeddings into the plane (Example)

Consider the following two plane graphs:

\includegraphics{g1}
The plane graph $ G_1$.
\includegraphics{g2}
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.




"example of planar graph with two different embeddings into the plane" is owned by archibal.
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Cross-references: graphs, implies, region, adjacent, face, isomorphic, multigraph, plane graphs

This is version 2 of example of planar graph with two different embeddings into the plane, born on 2004-03-31, modified 2004-03-31.
Object id is 5738, canonical name is ExampleOfPlanarGraphWithTwoDifferentEmbeddingsIntoThePlane.
Accessed 1891 times total.

Classification:
AMS MSC05C10 (Combinatorics :: Graph theory :: Topological graph theory, imbedding)

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