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Let $G$ and $Cay(A,S)$ be strongly regular graphs with the same parameters. Is it true that $G$ is a cayley graph?

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no, this is certainly not true. IIRC already on 25 vertices there is a family of 15 non-isomorphic s.r.g.'s with the same parameters, some of them Cayley graphs, some not: see http://www.win.tue.nl/~aeb/graphs/Paulus.html.

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    $\begingroup$ Latin square graphs (e.g. cs.yale.edu/homes/spielman/561/2009/lect23-09.pdf) will work; for each possible order there is a Cayley graph and (in general, $n\ge5$) examples that are not. $\endgroup$ Dec 21, 2012 at 13:48
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    $\begingroup$ For anyone who decides, as I did, to do a google search to find out the meaning of IIRC, ignore the entries on the "Illinois Interactive Report Card" and on the "International Integrated Reporting Council". $\endgroup$
    – Lee Mosher
    Dec 21, 2012 at 15:41
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    $\begingroup$ It means "Isn't It Really Cool" $\endgroup$ Dec 23, 2012 at 10:53
  • $\begingroup$ Yes, Brendan, this would work too :-) $\endgroup$ Dec 23, 2012 at 15:03

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