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The unique graphs with minimum distance spectral radius are determined in the set of connected graphs with given number of odd vertices and the unique trees with maximum distance spectral radius are determined in the set of trees with given number of odd vertices.The unique trees with maximum distance spectral radius are also determined in the class of trees with respectively given number of vertices of degree 3 and given number of vertices of degree at least 3,and the unique trees with respectively second minimum and second maximum distance spectral radius are determined in the class of trees with all vertices being odd.