Duplicates - additional observation

[David Wilson]

http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html

indicates that the number 6-regular graphs is 21609300, while the number of 7-regular graphs is 21609301.

Is this an error, coincidence or connection?
  ----- Original Message ----- 
  From: Ray Chandler 
  To: seqfan at ext.jussieu.fr 
  Sent: Monday, August 01, 2005 3:47 PM
  Subject: RE: Duplicates - which one is wrong?


  The connected 3-regular graphs determined by Brinkmann are listed in http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html

  This is the sequence A002851 which is described as connected cubic graphs with 2n nodes and lists this URL as a reference.  

  It's not clear to me what differentiates the "multigraph" sequences A000421/A005965 from the "graph" sequences A005638/A002851.

  A000421 and A002851 reference different pages of the same edition of CRC Handbook of Combinatorial Designs.  Can someone with access to that reference help to clarify the distinction.

  Ray




------------------------------------------------------------------------------
  From: JEREMY GARDINER [mailto:jeremy.gardiner at btinternet.com] 
  Sent: Monday, August 01, 2005 6:53 AM
  To: seqfan at ext.jussieu.fr
  Subject: Re: Duplicates - which one is wrong?


  Eric W. Weisstein. "Cubic Graph." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CubicGraph.html references A005638 and notes that, The connected 3-regular graphs have been determined by Brinkmann (1996) up to 24 nodes

  Brinkmann, G. "Fast Generation of Cubic Graphs." J. Graph Th. 23, 139-149, 1996. 

  Gordon Royle <gordon at csse.uwa.edu.au> wrote: 
    The two sequences

    http://www.research.att.com/projects/OEIS?Anum=A000421

    and

    http://www.research.att.com/projects/OEIS?Anum=A005965

    are both meant to be connected cubic multigraphs...


    Firstly, they are duplicates, and secondly, one of them is different 
    to the other - in particular there are apparently 506, or maybe 509, 
    connected cubic multigraphs on 12 vertices.
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