Degree Sequences (was Graphical Partitions)

[Frank Ruskey]

Hi Gordon and Neil,

I have verified your sequence values for A095268, and offer two more:
a(21) =  28723877732
a(22) = 111236423288
So the pattern of a(n) even for n odd continues.  Proof?

A couple of suggestions regarding A095268
- Remove my comment, but add a link to
   http://www.cs.uvic.ca/~ruskey/Publications/AlleyCat.html
- Delete the MATHEMATICA program.  It just appears to be filtering
   a list of graphs, which is a really horrible way of generating the
   numbers. (But I don't know Mathematica, so you may want to
   check with an expert.)
- Delete the link to Mathworld "Graphical Partitions".  The definition
   given there is non-standard.  If you want a link into Mathworld
   it would be better to use 
http://mathworld.wolfram.com/DegreeSequence.html

Cheers,
Frank




Gordon Royle wrote:
> Dear seqfansters
> 
> The sequence http://www.research.att.com/~njas/sequences/A095268 that 
> was discussed recently gives the number of different degree sequences 
> from all the n-vertex graphs with no isolated vertices.
> 
> [BTW, I think the offset should be "2" not "1"]
> 
> One thing that I noticed while extending this was the behaviour of the 
> ratio a(n+1)/a(n) which is as follows:
> 
> 
> 2
> 3.5
> 2.857
> 3.550
> 3.380
> 3.629
> 3.614
> 3.702
> 3.718
> 3.756
> 3.773
> 3.794
> 3.808
> 3.822
> 3.833
> 3.843
> 3.851
> 3.859
> 
> 
> Question: does a(n+1)/a(n) tend to a limit? If so, is it 4? If so, 
> why... anyone have even a heuristic argument as to why there should be 4 
> times as many degree sequences on n+1 vertices as there are on n?
> 
> Cheers
> 
> Gordon


-- 
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Frank Ruskey         e-mail: (last_name)(AT)cs(DOT)uvic(DOT)ca
Dept. of Computer Science        fax:    250-472-5708
University of Victoria           office: 250-472-5794
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