1
$\begingroup$
    o 
    |
o---o---o---o
 \         /
  o       o
   \     / \
    o   o   \
   / \ /     o
  /   o
 o

(I apologise for the poor diagram unable to insert an image yet)
o represents a node and the dashed lines are arcs
My question is why are there 6 automorphisms for this graph? I can only identify 3 due to rotational symmetry.

$\endgroup$
  • 5
    $\begingroup$ there are also three reflections. Your diagram does not show those well, try drawing the main triangle as a circle $\endgroup$ – Will Jagy Mar 28 at 0:39
  • $\begingroup$ Oh right I see it now, thank you! $\endgroup$ – Kham Mar 28 at 0:43
  • $\begingroup$ @WillJagy If you wanted to post that as an answer, I’d happily (+1) $\endgroup$ – Santana Afton Mar 28 at 2:40
  • $\begingroup$ @SantanaAfton I put a picture $\endgroup$ – Will Jagy Mar 28 at 3:05
2
$\begingroup$

This one has few enough points that we can draw a picture with the same geometric symmetries as the graph automorphisms. A rare luxury

enter image description here

$\endgroup$
  • $\begingroup$ As a note to the OP: the way Will Jagy has drawn the graph here should ring “dihedral group” bells for you (if you’re familiar with it). $\endgroup$ – Santana Afton Mar 28 at 3:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.