Using OEIS...

[Jon Awbrey]

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if this is graph reconstruction, then my advice
is to turn 180 degrees, and run as fast you can
in the other direction.

ja

p.s. same advice applies to matroids.

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Gordon Royle wrote:
> 
> A real-life story of using OEIS..
> 
> I am currently working on a problem where graphs that
> are obtained from smaller graphs by replacing a vertex
> by a clique (and adjoining the neighbours of the vertex
> to each element of the clique) need not be considered.
> In other words, I just need the "reduced" graphs where
> no two adjacent vertices u and v have the property that
> N(u) - {v} = N(v) - {u}.
> 
> So I calculated these (connected) graphs on up
> to 10 vertices or so, and got the numbers:
> 
> 3,11,61,507,7442,197772,9808209
> 
> As usual, bung them into OEIS and up comes the sequence A004108
> which is connected graphs without endpoints -- in other words,
> graphs without vertices of degree 1.
> 
> So, what is the connection between these "reduced" graphs and having
> minimum degree two (they are not the same set of graphs) ...
> 
> It turns out that there is a simple, but cute, bijection between the
> two classes of graphs that might make a nice little student exercise ...
> 
> I will leave it as a puzzle for anyone interested in some gentle mental
> exercise ... and I'll add the answer in a few days as a comment to A004108.
> 
> All the best
> 
> Gordon
> 
> PS I am still looking for someone who can tell me what
> a "basic circuit of nullity n" is, and whether it really
> is just a 3-connected cubic graph.....
> 
> --
> Dr. Gordon F Royle, http://www.csse.uwa.edu.au/~gordon, gordon at csse.uwa.edu.au
> --

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