[seqfan] Re: A064513, A058201, and the graph degree/diameter problem.

[Allan Wechsler]

The Wikipedia article I referenced earlier believes the 50 number, and
provides a lot of references to journal articles. Anyone with access to a
university library should be able to source the a(7) = 50 claim. Apparently
the biggest known diameter 2 graph with degree 8 has only 57 vertices,
which seems low to my intuition. Pushing this number higher might be a good
student project.
On Nov 17, 2015 12:57 PM, "Neil Sloane" <njasloane at gmail.com> wrote:

> Allan, Chris,
> Thanks for those comments.
> I "deaded" A058201, and I'm revising A064513.
>
> My old notes there say that it is known that a(7)=50. Do you believe that?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Tue, Nov 17, 2015 at 11:03 AM, Allan Wechsler <acwacw at gmail.com> wrote:
>
> > I apologize for getting the values backwards. It is as Chris Thompson
> says:
> > the old sequence says 25 and is wrong, and the new one says 24, and is
> > right, agreeing with all online sources I have consulted.
> >
> > But a(2) still ought to be 5, not 4.
> >
> > On Tue, Nov 17, 2015 at 9:37 AM, Chris Thompson <cet1 at cam.ac.uk> wrote:
> >
> > > On Nov 17 2015, Allan Wechsler wrote:
> > >
> > > [... snipped...]
> > >
> > >> Wikipedia has articles on the degree/diameter problem. The first
> column
> > of
> > >> their table (
> > >>
> > >
> > >
> >
> https://en.wikipedia.org/wiki/Table_of_the_largest_known_graphs_of_a_given_diameter_and_maximal_degree
> > >
> > >> ) gives values 2, 5, 10, 15, 25, 32, 50. So their a(5) agrees with the
> > >> later
> > >> sequence on OEIS, but their a(2) (and *my* a(2), for that matter!)
> > >> disagrees with *both* versions on OEIS.
> > >>
> > >
> > > I read the Wikipedia page as saying that a(5) = 24 - admittedly the
> dark
> > > blue background could easily lead to misreading!
> > >
> > > In any case, that agrees with the EJC Dynamic Survey (updated 2013).
> The
> > > Wikipedia link to that seems to be broken: a working one is
> > >
> > > http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS14
> > >
> > > This also confirms a(6) = 32 as optimal.
> > >
> > > --
> > > Chris Thompson
> > > Email: cet1 at cam.ac.uk
> > >
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