Laplacian Distribution and Domination

Let denote the number of Laplacian eigenvalues of a graph G in an interval I, and let denote its domination number. We extend the recent result , and show that isolate-free graphs also satisfy . In pursuit of better understanding Laplacian eigenvalue distribution, we find applications for these inequalities. We relate these spectral parameters with the approximability of , showing that . However, gamma(G) <= m(G)[2, n] <= (c + )gamma(G) for c-cyclic graphs, c >= 1. For trees T, gamma(T) <= m(T)[2, n] < 2 gamma(G).