As the title says, let $S$ be the nonempty set of strongly regular graphs with given parameters. Must $S$ contain vertex transitive graph?


I suspect the most likely counterexample would be $|S|=1$.



Let $S$ be the nonempty set of strongly regular graphs with given parameters. Must $S$ contain vertex transitive graph?
There are exactly 10 strongly regular graphs with parameters (26,10,3,4), none of which are vertex-transitive. The graphs can be found on [Ted Spence's webpage](http://www.maths.gla.ac.uk/~es/srgraphs.php). 


