Let n≥k≥2 be two integers and S a subset of {0,1,…,k−1}.
The graph JS(n,k) has as vertices the k-subsets of the n-set
[n]={1,…,n} and two k-subsets A and B are adjacent if ∣A∩B∣∈S. In this paper, we use Godsil-McKay switching to prove that for m≥0, k≥max(m+2,3) and S={0,1,...,m}, the graphs JS(3k−2m−1,k)
are not determined by spectrum and for m≥2, n≥4m+2 and S={0,1,...,m} the graphs JS(n,2m+1) are not determined by spectrum. We
also report some computational searches for Godsil-McKay switching sets in the
union of classes in the Johnson scheme for k≤5.Comment: 9 pages, no figures, 3 tables; 2nd version contains improved results
compared to the 1st versio