Wanna run that on connected graphs? I get the correct sequence out to n=9 for
def ec(n)
c = 0
for g in graphs(n):
if g.is_connected() and g.line_graph().is_vertex_transitive():
c+= 1
return c
On Mon, Oct 29, 2012 at 11:37 AM, Jernej Azarija <azi.std...@gmail.com> wrote:
> Hello!
>
> Yes but this appears to be even more bogus. Consider this:
>
> ==
> def ec(n):
> c = 0
> for el in graphs.nauty_geng(str(n)):
> if (el.line_graph()).is_vertex_transitive():
> c+=1
> return c
> ==
>
> sage: ec(7)
> 27
> sage: ec(8)
> 39
>
> But there are 26 and 40 edge-transitive graphs on 7 and 8 nodes
> respectively. It appears as if something is wrong with the computation of
> the automorphism group of a graph.
>
> Can someone comment on that?
>
>
>
>
>
>
>
>
> On Monday, 29 October 2012 19:29:56 UTC+1, Tom wrote:
>>
>> I use G.line_graph().is_vertex_transitive()
>>
>> On Mon, Oct 29, 2012 at 7:12 AM, Jernej Azarija <azi.s...@gmail.com>
>> wrote:
>> > Hello!
>> >
>> > I am slowly implementing a patch that will provide some features for
>> > symmetry testing of graphs.
>> >
>> > However I am already puzzled by the following attempt at testing for
>> > edge-transitive graphs. Here is a straightforward textbook
>> > implementation
>> > (the presented code omits the exceptional treatment of the singleton
>> > graph)
>> >
>> > ===
>> > def is_edge_transitive(self):
>> >
>> > A,T = self.automorphism_group(translation=True)
>> > for (x,y,_) in self.edges():
>> > acts = set([])
>> > for g in A:
>> > a,b = g(T[x]),g(T[y])
>> > acts.add((a,b) if a < b else (b,a))
>> > if len(acts) == self.size():
>> > return True
>> > return False
>> > ===
>> >
>> > Testing the code (Petersen, Gray and path graph) it appears as if the
>> > results are correct. But considering the following function computing
>> > the
>> > number connected edge transitive graphs of given order
>> >
>> > ===
>> > def ecc(n):
>> > c = 0
>> > for el in graphs.nauty_geng(str(n)+ " -c "):
>> > if el.is_edge_transitive():
>> > c+=1
>> > return c
>> > ===
>> >
>> > we observe that
>> >
>> > sage: [ecc(i) for i in xrange(2,9)]
>> > [1, 2, 3, 4, 6, 5, 8]
>> >
>> > which does not coincide with the data provided at oeis:
>> > http://oeis.org/A095424/list . The difference gets even bigger if we
>> > count
>> > all edge-transitive graphs instead of just connected.
>> >
>> > Anyone happens to see the flaw in the is_edge_transitive method?
>> >
>> > Best,
>> >
>> > Jernej
>> >
>> > --
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>> >
>> >
>
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