直径为4的整树新类

摘要

An integral graph is a graph of 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. These results generalize some results of Wang, Li and Zhang (see Families of integral trees with diameters 4, 6 and 8, Discrete Applied Mathematics, 2004, 136: 349-362).%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.通过求解某些确定的丢番图方程,构造了具有无穷多个这样的整树新类,推广了王力工、李学良和张胜贵发表的文章(见Families of integral trees with diameters 4,6 and 8,DiscreteApplied Mathematics,2004,136:349-362)的一些结论.