I need a few examples of graphs that are strongly regular as well as rigid, i.e., have only the trivial automorphism. Any references to relevant literature would be appreciated. Thanks.


At Ted Spence's web page http://www.maths.gla.ac.uk/~es/srgraphs.php you can find all the strongly regular graphs on 25 and 26 vertices, and these include examples of asymmetric graphs. (No srg on fewer than 25 vertices is asymmetric.)

You get more examples as Latin square graphs. Take an $n\times n$ Latin square (with $n\ge 6$). Define the vertices of the graph to be the $n^2$ cells of the square, and declare two cells to be adjacent if they are in the same row, or in the same column, or have the same content. Most Latin squares will work.

You can also construct srgs on the triples of Steiner triple systems (adjacent if they overlap), and Babai proved that almost all of these are asymmetric.

  • $\begingroup$ Is it easy to see which ones of these are asymmetric? $\endgroup$ – Pawan Aurora May 2 '13 at 17:37
  • 1
    $\begingroup$ Yes, you pipe them through nasty, or use sage. $\endgroup$ – Chris Godsil May 2 '13 at 17:51

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