Minimum supports of eigenfunctions of Johnson graphs

We study the weights of eigenvectors of the Johnson graphs J(n,w). For any i∈{1,…,w} and sufficiently large n,n≥n(i,w) we show that an eigenvector of J(n,w) with the eigenvalue λi=(n−w−i)(w−i)−i has at least 2in−2iw−i nonzeros and obtain a characterization of eigenvectors that attain the bound.