Domination number and Laplacian eigenvalue distribution

Let mG(I)mG(I) denote the number of Laplacian eigenvalues of a graph GG in an interval II. Our main result is that for graphs having domination number γγ, mG[0,1)≤γmG[0,1)≤γ, improving existing bounds in the literature. For many graphs, mG[0,1)=γmG[0,1)=γ, or mG[0,1)=γ−1mG[0,1)=γ−1.