# What are the eigenvectors of the graph Laplacian of a Johnson graph J(n,k)?

The spectral properties of Johnson graphs are known. However I also like to know more about their eigenvectors. Are there any results on the eigenvectors of the graph Laplacians of these Johnson graphs?

• Experimentally, $J(n,k)$, which has $\binom nk$ vertices, has $\min(k,n-k)+1$ distinct eigenvalues that are all integers. The smallest is $-\min(k,n-k)$, and of course the largest is the degree. I tested all cases to $n=12$. – Brendan McKay Sep 22 '17 at 5:56