Abstract: By using edge-moving operations and the Perron-Frobenius theorem, we discussed the problem of the spectral radius of the complement distance  of tree graph.  We determined the unique trees with maximum  and minimum spectral radii of  the complementary distance, respectively, and  determined the graph with the minimum spectral radius of  the  complementary distance in the complementary graph of the tree,  as well as the graph with  the i-th largest spectral radius of complementary distance, where  i=1,2,…,(n-2)/2.

Key words: spectral radius of complementary distance, complementary distance matrix, distance matrix, extremal graph