Count the number of automorphisms in the graph

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SUMMARY

The discussion focuses on counting the number of automorphisms in a given graph. The user calculates the total by considering the arrangements of vertices (a, m, b) which can be permuted in 3! (6) ways, and the pairs (g, h) and (e, d) which can be arranged in 4 ways. The final calculation results in a total of 24 automorphisms, confirming the user's understanding of the problem. The graph in question is not attached, but the methodology for counting automorphisms is clearly outlined.

PREREQUISITES
  • Understanding of graph theory concepts, specifically automorphisms.
  • Familiarity with permutations and combinations.
  • Basic knowledge of vertex arrangements in graphs.
  • Experience with mathematical problem-solving techniques.
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  • Study the concept of graph automorphisms in detail.
  • Learn about the application of group theory in graph theory.
  • Explore advanced permutation techniques and their implications in combinatorial problems.
  • Investigate software tools for visualizing graph structures and automorphisms.
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Students studying graph theory, mathematicians interested in combinatorial structures, and educators teaching advanced mathematics concepts.

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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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Just FYI, the graph is NOT attached.
 
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