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example of planar graph with two different embeddings into the plane
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(Example)
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Consider the following two plane graphs:
The plane graph  .
The plane graph  .
Clearly the multigraph associated with each of these plane graphs is the same, but the two plane graphs are not isomorphic: in , every face is adjacent to the central region, while in there is no face adjacent to every other. This also implies that their dual graphs are non-isomorphic.
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"example of planar graph with two different embeddings into the plane" is owned by archibal.
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(view preamble | get metadata)
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 MSC: | 05C10 (Combinatorics :: Graph theory :: Topological graph theory, imbedding) |
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Pending Errata and Addenda
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