# Finding the automorphism group of a graph

Let me denote the graph in the picture by $$\Gamma$$ and I will refer to the points as numbers $$1-9$$. I need to find Aut($$\Gamma$$).

Looking at this graph, it seems that there can be a permutation on the outer most edges 17 and 96, then both, then a symmetric mirror of this graph. So we have id,(17),(96),(17)(96),(25)(16)(97),(25)(19)(67),(25)(16)(97)(34),(25)(19)(67)(34). Is this correct? are there any other automorphisms I'm missing? thanks.

• Why are you using a different labelling for vertices than the one on the picture? What is the correspondence? – verret Apr 16 at 9:45
• The automorphism group of this graph does indeed have order $8$. – Derek Holt Apr 16 at 9:49
• @verret A-G as 1-9. It's easier like this. – mandella Apr 16 at 9:54