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The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. Among nvertex trees, the star has greatest nullity (equal to n − 2). We generalize this by showing that among n-vertex trees whose vertex degrees do not exceed a certain value D, the greatest nullity is n − 2 (n − 1)/D . Methods for constructing such maximum-nullity trees are described.doi:10.1016/j.laa.2004.10.024 fatcat:kzo72iz6jbcbxpc4zlb6dedqpu