I recently saw this post from Ed Pegg on Math Stack Exchange about integral graphs with trivial automorphism groups. I am interested in trying to construct smaller such graphs - at the very least, I would like to learn about the machinery involved. What are some known results on the relationship between the automorphisms of a graph and the spectrum of the graph? I am sure there are many known results but I haven't found a good online resource yet. I wouldd appreciate any explanations and or references. Thanks!
2026-03-25 23:22:52.1774480972
Known results on the relationship between automorphisms and spectrum of a graph?
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Chan and Godsil have an excellent survey here. They include an exposition on equitable partitions, which was the example that immediately came to mind. Cvetkovic, Rowlinson, and Simic also treat equitable partitions in their London Mathematical Society text on spectral graph theory.