[seqfan] Re: Number of Euler graphs: A002854 or something else?

[Max Alekseyev]

On Thu, Jan 28, 2010 at 11:59 AM, N. J. A. Sloane <njas at research.att.com> wrote:
> Max,  I think you have misunderstood the definition of Euler graph.

I've just followed the definitions given in MathWorld and Wikipedia.
In particular, MathWorld defines Eulerian Graph as "a graph containing
an Eulerian cycle."
http://mathworld.wolfram.com/EulerianGraph.html

That's especially confusing since MathWorld and A002854
cross-reference each other.

> An Euler graph is a graph with every node having even degree.
>
> I will add a comment to A002854 to clarify this.

That settles things up. Thanks!

> Your definition :
>
>> Let us assume the conventional definition of Euler graphs:
>> a graph is Euler if there exists an Euler cycle, i.e., a cycle that
>> goes through every edge in the graph exactly once.
>
> is not right.

Well, at least I did not invent this definition.

Regards,
Max