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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