# [seqfan] Re: graphs with odd degrees

Neil Sloane njasloane at gmail.com
Sun Apr 8 04:11:07 CEST 2012

```"Graph" almost always means "simple graph, without self-loops or parallel
edges" in the mathematical literature (including the OEIS). On the other
hand it does not necessarily mean connected. So I think the definition is
perfectly clear as is!

I have pictures of the 16 6-node examples  - i'll

Neil

On Sat, Apr 7, 2012 at 8:44 PM, David Wilson <davidwwilson at comcast.net>wrote:

> It is clear that we cannot allow repeated edges, since then there would be
> an infinite number of 2-vertex graphs (any graph in which the two vertices
> are connected by an odd number of edges). So we should probably mention
> that repeated edges are verboten.
>
> Don't we need to specify that edges cannot be duplicated?
>
> The 1 counts the 2-vertex graphs, specifically the complete graph.
>
> The 3 counts the 4-vertex graphs, which would include the complete graph,
> the tree with root of order 3, and the disconnected graph consisting of two
> complete 2-vertex graphs. So we should probably mention that disconnected
> graphs are permissible.
>
> I would feel better if someone could draw out the 16 graphs on 6 vertices.
>
>
>
> On 4/6/2012 9:59 AM, Neil Sloane wrote:
>
>> The convention in the OEIS is that if a sequence
>> has every other term zero, we omit the zeros.
>>
>> So the OEIS version of this sequence should be
>> 1,3,16,243,...
>>
>> Neil
>>
>
>
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Dear Friends, I will soon be retiring from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA