# Count the number of automorphisms in the graph

## Homework Statement

I had a different problem before about this and I figured it out. I'd like to know if I'm doing this one correctly as well.
Count the number of automorphisms in the graph.
The graph is attached, now.

## The Attempt at a Solution

I know I can rearrange the (a,m,b) 3! ways. I also know that I can only arrange (g,h) and (e,d) 4 ways. So, for each arrangement of (a,m,b) I have 4 arrangements of (g,h) and (e,d). Then 6*4=24 total.

Have I got this sorted out correctly?

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