# [seqfan] Re: graphs with odd degrees

David Wilson davidwwilson at comcast.net
Sun Apr 8 02:44:35 CEST 2012

```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

```