On 2012-10-30, Tom Boothby <tomas.boot...@gmail.com> wrote: > Oops, didn't see your reply before I posted. Not counting the empty > graph is very very strange. At the very least OEIS needs to be > updated to have a proper definition to warn people that the empty > graph is excluded.
it's a tricky question whether groups can be allowed to act on the empty set. If they aren't, then the empty graphs must be excluded. I prefer to think of transitive actions having one orbit, while allowing empty sets needs a change here: 0 or 1 orbits... Allowing actions on empty sets loses you the 1-1 correspondence between the transitive actions and the actions on cosets of subgroups. So there is a lot to be lost here. Dima > > > > On Tue, Oct 30, 2012 at 4:23 AM, Dima Pasechnik <dimp...@gmail.com> wrote: >> On 2012-10-30, Jernej Azarija <azi.std...@gmail.com> wrote: >>> ------=_Part_1698_7171753.1351582604933 >>> Content-Type: text/plain; charset=ISO-8859-1 >>> >>> On Monday, 29 October 2012 22:49:03 UTC+1, Tom wrote: >>>> >>>> Here's a list of 21 edge-transitive graphs on 6 vertices. >>>> >> [...] >>>> They've all got 6 vertices. They're all edge transitive. That means >>>> Weisstein's list is wrong. >> >> no, not really. He just doesn't count empty graphs. Somewhere on >> http://mathworld.wolfram.com/Edge-TransitiveGraph.html >> you can read: >> >> "Counting empty graphs as edge-transitive, the numbers of edge-transitive >> graphs on , 2, ... nodes are 1, 2, 4, 8, 12, 21, 27, .... " >> >> So it's a misunderstand related to definitions used, rather than >> a bug in someone's code, it seems. >> >> Dima -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
