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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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up vote 6 down vote accepted

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

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Latin square graphs (e.g. 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

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