missing sequence? number of embeddings of planar graphs

N. J. A. Sloane njas at research.att.com
Sat Mar 10 04:25:04 CET 2007

side of the triangle or not:
        / \
      /     \
     o       o
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From: Brendan McKay <bdm at cs.anu.edu.au>
To: "N. J. A. Sloane" <njas at research.att.com>
Cc: seqfan at ext.jussieu.fr
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Subject: Re: missing sequence? number of embeddings of planar graphs
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I have #2 up to 14 vertices (3807081193879), computed by myself
and Gunnar Brinkmann.  Presumably #1 follows by the appropriate

There are actually two natural variants, depending on whether
mirror images are counted as equivalent.

Looking at our paper, it seems like lots of things in there are not
in OEIS. Bad us. Would anyone like to volunteer to do the packaging
and transformations? I really don't have time. It would help to
be able to understand basic terminology for graphs and planar
embeddings. Expect a few hours of work. Of course I'll help to get
the definitions straight.


* N. J. A. Sloane <njas at research.att.com> [070310 14:25]:
> Dear Seqfans,
> I suspect these two sequences may be missing from the OEIS:
> 1.  Number of planar graphs on n unlabeled nodes,
> where we count each graph according to the number
> of its embeddings into the sphere.
> For example, this graph on 5 nodes has 2 embeddings,
> dpending on whether the two "whiskers" are on the same
> side of the triangle or not:
>          o
>         / \
>        o---o
>       /     \
>      o       o
> 2. Same question for connected planar graphs
> Could someone work out the first few terms?
> Neil
> (Planar graphs are in A005470, connected ditto in A003094)

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