Abstract: An integral graph is a graph which all the eigenvalues of its adjacency matrix are integers. This paper investigates integral trees of diameter 4. Many new classes of such integral trees are constructed infinitely by solving some certain Diophantine equations.

Key words: integral trees, characteristic polynomial, diophantine equation, graph spectrum

摘要： 整图是指图的邻接矩阵的特征值全为整数的图。研究了直径为4的整树。通过求某些特定的丢番图方程，构造了具有无穷多个这样的整树新类。

关键词: 整树, 特征多项式, 丢番图方程, 图的谱