On the coefficients of the Laplacian characteristic polynomial of trees

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Let the Laplacian characteristic polynomial of an n-vertex tree T be of the form ?(T, ?) = ?nk=0(-l)n-k ck(T)?k . Then, as well known, C0(T) = 0 and c1 (T) = n. If T differs from the star (Sn) and the path (Pn), which requires n ? 5, then c2(Sn} < C2(T) < C2(Pn) and c3(Sn) < c3(T) < c3(Pn). If n = 4, then c3(Sn) = c3(Pn).