直径为4的整树新类

运筹学学报 ›› 2011, Vol. 15 ›› Issue (2): 19-27.

直径为4的整树新类

王力工，张政

出版日期:2011-06-15 发布日期:2011-06-15

Some New Families of Integral Trees of Diameter Four

WANG Li-Gong, Zhang-Zheng

Online:2011-06-15 Published:2011-06-15
Supported by:
Supported by the National Natural Science Foundation of China　(No. 10871158), the Natural Science Foundation of Shaanxi　Province (No. SJ08A01) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

摘要/Abstract

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, it Discrete Applied Mathematics, 2004, 136: 349-362)的一些结论.

关键词: 整树, 特征多项式, 丢番图方程, 图的谱

Abstract: An integral graph is a graph of which all the eigenvalues of its　adjacency matrix are integers. This paper investigates itegral trees of diameter 4.　Many new classes of such integral trees are cnstructed ifinitely 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).

Key words: Operations research, integral tree, chracteristic polynomial, diophntine equation, graph spectrum

中图分类号:

王力工, 张政. 直径为4的整树新类[J]. 运筹学学报, 2011, 15(2): 19-27.

WANG Li-Gong, Zhang-Zheng. Some New Families of Integral Trees of Diameter Four[J]. Operations Research Transactions, 2011, 15(2): 19-27.