中文摘要：

利用图谱理论对树的补图的奇异性进行了研究,得到了直径为n-1,n-2和n-3的树的补图的奇异性的一般判断方法,推广了前人的研究成果.

英文摘要：

The singularity of the complement graphs of trees is studied by spectral graph theory.The general judgement methods for the singularity of the complement of trees with diameter n？1,n？2 or n？3 are respectively established,which generalizes the results of predecessors.