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.
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）.
出处
《运筹学学报》
CSCD
2011年第2期19-27,共9页
Operations Research Transactions
基金
Supported by the National Natural Science Foundation of China(No.10871158)
the Natural Science Foundation of Shaanxi Province(No.SJ08A01)
the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
关键词
整树
特征多项式
丢番图方程
图的谱
integral tree
characteristic polynomial
diophantine equation
graph spectrum
