\         /
  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.

  • 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

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

  • $\begingroup$ 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

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