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<DIV><FONT size=2><A
href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html</A></FONT></DIV>
<DIV><FONT face="Times New Roman" size=2></FONT> </DIV>
<DIV><FONT face="Times New Roman" size=2>indicates that the number 6-regular
graphs is 21609300, while the number of 7-regular graphs is
21609301.</FONT></DIV>
<DIV><FONT face="Times New Roman" size=2></FONT> </DIV>
<DIV><FONT face="Times New Roman" size=2>Is this an error, coincidence or
connection?</FONT></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=Ray.Chandler@comcast.net href="mailto:Ray.Chandler@comcast.net">Ray
Chandler</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=seqfan@ext.jussieu.fr
href="mailto:seqfan@ext.jussieu.fr">seqfan@ext.jussieu.fr</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, August 01, 2005 3:47
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> RE: Duplicates - which one is
wrong?</DIV>
<DIV><BR></DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005>The connected 3-regular graphs determined by
Brinkmann are listed in <A
href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html</A><A
href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html#CRG"></A></SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005>This is the sequence A002851 which is described as
connected cubic graphs with 2n nodes and lists this URL as a reference.
</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005>It's not clear to me what differentiates the
"multigraph" sequences A000421/A005965 from the "graph" sequences
A005638/A002851.</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><SPAN class=421071819-01082005><FONT color=#0000ff
size=2>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.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005>Ray</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2><SPAN
class=421071819-01082005></SPAN></FONT> </DIV><BR>
<DIV class=OutlookMessageHeader lang=en-us dir=ltr align=left>
<HR tabIndex=-1>
<FONT face=Tahoma size=2><B>From:</B> JEREMY GARDINER
[mailto:jeremy.gardiner@btinternet.com] <BR><B>Sent:</B> Monday, August 01,
2005 6:53 AM<BR><B>To:</B> seqfan@ext.jussieu.fr<BR><B>Subject:</B> Re:
Duplicates - which one is wrong?<BR></FONT><BR></DIV>
<DIV></DIV>
<DIV>
<P class=citation>Eric W. Weisstein. "Cubic Graph." From <A
href="http://mathworld.wolfram.com/" target=_blank><I><FONT
color=#003399>MathWorld</FONT></I></A>--A Wolfram Web Resource. <A
href="http://mathworld.wolfram.com/CubicGraph.html" target=_blank><FONT
color=#003399>http://mathworld.wolfram.com/CubicGraph.html</FONT></A>
references <A class=Hyperlink
href="http://www.research.att.com/projects/OEIS?Anum=A005638"
target=_blank><FONT color=#003399>A005638</FONT></A> and notes that, The
connected 3-regular graphs have been determined by Brinkmann (1996) up to 24
nodes</P>
<P class=Reference>Brinkmann, G. "Fast Generation of Cubic Graphs." <I>J.
Graph Th.</I> <B>23</B>, 139-149, 1996. </P><B><I>Gordon Royle
<gordon@csse.uwa.edu.au></I></B> wrote:
<BLOCKQUOTE class=replbq
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff 2px solid">The
two
sequences<BR><BR>http://www.research.att.com/projects/OEIS?Anum=A000421<BR><BR>and<BR><BR>http://www.research.att.com/projects/OEIS?Anum=A005965<BR><BR>are
both meant to be connected cubic multigraphs...<BR><BR><BR>Firstly, they are
duplicates, and secondly, one of them is different <BR>to the other - in
particular there are apparently 506, or maybe 509, <BR>connected cubic
multigraphs on 12 vertices.<BR></BLOCKQUOTE></DIV></BLOCKQUOTE></BODY></HTML>