On Wednesday, 24 August 2016 02:00:03 UTC+10, Dima Pasechnik wrote:
>
> In this case your graphs give rise to Hadamard matrices (take Seidel 
> adjacency matrix), so if you get nonisomorphic Hadamard matrices then you 
> get nonisomorphic graphs, but not the other way around, generally speaking.
> Although isomorphism of Hadamard matrices is probably harder...


See  
https://github.com/penguian/Boolean-Cayley-graphs/blob/master/README.md for 
some of the background and references.

I am developing Sage code to enumerate the Cayley graphs of those bent 
functions whose value at 0...0 is 0. 
Each such graph is strongly regular. See (e.g.) 
http://ieeexplore.ieee.org/document/954512/
The code explores the bent functions within each extended Affine 
equivalence class. Actually, the extended *translation* equivalence class 
gives all isomorphism classes of Cayley graphs.

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