[seqfan] Re: A002831 incompatible with A002830

[Sean A. Irvine]

On 09/09/14 15:25, Neil Sloane wrote:
> PS
> Sean, What about the case when the nodes are labeled, A006712
> and A006713 - can you check them?

I think the later terms of A006712 and A006713 are also incorrect.  The difference in a(5) (154103040-150474240 = 3628800) is consistent with one symmetry being overlooked in a single connected graph when computing the number of edge-colorings.

Current  A006712: 6, 480, 197820, 154103040, 215643443400
Current  A006713: 6, 480, 196560, 153498240, 214951968000

Computed A006712: 6, 480, 197820, 150474240, 208857587400
Computed A006713: 6, 480, 196560, 149869440, 208166112000

Unlike A002830 and A002831 it will not be feasible with my current back-tracking search to further extend these sequences.  The slow part is computing the number of possible labelings for each candidate graph.  I believe this should be possible with nauty provided I can extract the size of the automorphism group for each graph, since then the labellings should be n!/|Aut(G)| for n vertices, but I haven't yet had time to explore this.

Sean.