We consider a class of random graphs, called random brushes, which are constructed by adding linear graphs of random lengths to the vertices of Z viewed as a graph. We prove that for d = 2 all random brushes have spectral dimension ds = 2. For d = 3 we have 5 2 ≤ ds ≤ 3 and for d ≥ 4 we have 3 ≤ ds ≤ d.
