Duplicates - which one is wrong?

[Ray Chandler]

The connected 3-regular graphs determined by Brinkmann are listed in
http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html <http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html#CRG> 
 
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  <http://mathworld.wolfram.com/> MathWorld--A Wolfram Web Resource.
<http://mathworld.wolfram.com/CubicGraph.html> http://mathworld.wolfram.com/CubicGraph.html references
<http://www.research.att.com/projects/OEIS?Anum=A005638> 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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