Is there a repository of cospectral non-isomorphic graphs available somewhere?


I am looking for list of $0/1$ adjacency matrix pairs that can be input data in tools such as MATLAB.



Database of adjacency matrices on cospectral non-isomorphic graph pairs
The simplest source of cospectral graphs is lists of strongly regular graphs, lots of which are easily available from Ted Spence's web page at <http://www.maths.gla.ac.uk/~es/srgraphs.php>.


Otherwise you can use Sage to generate small graphs (up to 10 or so vertices) and then filter out cospectral pairs or groups. I expect the built in Sage function for cospectral pairs just wraps this up.


I don't know what you are doing with them, but I'd probably recommend choosing the computational tool based on what you need, rather than specifying Matlab in advance. If you're working with 64 vertex graphs you'll need full symbolic computation with arbitrary length integers and you'll want to avoid, or be very very careful, in finding eigenvalues numerically.


