# Strongly regular cayley graphs

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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## 1 Answer

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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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. –  Chris Godsil Dec 21 '12 at 13:48
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". –  Lee Mosher Dec 21 '12 at 15:41
It means "Isn't It Really Cool" –  Brendan McKay Dec 23 '12 at 10:53
Yes, Brendan, this would work too :-) –  Dima Pasechnik Dec 23 '12 at 15:03