[GAP Forum] vertex-transitive non-Cayley graphs on 16 vertices

[Gordon Royle]

Data on transitive groups is available at

http://staffhome.ecm.uwa.edu.au/~00013890/remote/trans/index.html

Apologies for the constantly changing URL, but our university IT is constantly restructured…

The file for noncay16 contains these lines

Os`a`_HA_OA?OJGF?x?Hg
O~a at OtJP?I_rAC at Gc@W_N
O|qC?{eH_wbSKOQ[gdqC{
O~i]ED[ZGM_zK`KQ`TWRN
OvytUFCFyNC{E\FeMHzP]
O~z\dzEqjdngBlB]c\we~
O}rtt]]}NqL}VyL}FRyJ~
O~~~ffVm~[Pn^RFnh^xN

Each line is a graph stored in a special format devised by Brendan McKay and called “g6” or “graph6”.

The computer algebra system Sage (sagemath.org<http://sagemath.org>) can read g6 and then draw you a picture or whatever else you want, or you can download a g6 reader from Brendan’s own website.

Enjoy

Gordon


On 27 Aug 2014, at 9:00 pm, Petr Savicky <savicky at cs.cas.cz<mailto:savicky at cs.cas.cz>> wrote:

Dear GAP Forum:

I am interested in vertex-transitive graphs on n=2^k
vertices, which are not Cayley graphs. According to
the available literature, such graphs exist for every
k \ge 4. In particular, there are 8 such graphs
for n=16.

Are some of these graphs available in GAP or GRAPE
package?

I did not find any library of graphs in the base part
of GAP and GRAPE web documentation. However, there
may be additional resources, which I am not aware of.

Thank you in advance for any information concerning
these graphs.

Petr Savicky.


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Professor Gordon Royle
School of Mathematics and Statistics
University of Western Australia
Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>