[1]徐新萍,张丽丽.有关树的最大特征值的上界[J].南京师大学报(自然科学版),2010,33(04):1-5.
　Xu Xinping,Zhang Lili.The Upper Bound of the Largest Eigenvalue on the Trees[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(04):1-5.
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有关树的最大特征值的上界()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第33卷
期数:
2010年04期
页码:
1-5
栏目:
数学
出版日期:
2010-12-20

文章信息/Info

Title:
The Upper Bound of the Largest Eigenvalue on the Trees
作者:
徐新萍1;  张丽丽2
1. 江苏教育学院数学与信息技术学院, 江苏南京210013 2. 河海大学计算机与信息学院, 江苏南京210098
Author(s):
Xu Xinping1; Zhang Lili2
1.School of Mathematics and Information Technology,Jiangsu Institute of Education,Nanjing 210013,China 2. C ollege of C ompu ter and In form ation, H ohaiUn iversity, Nan jing 210098, Ch ina
关键词:
树;  特征值;  上界
Keywords:
trees;  e ig envalue;  upper bound
分类号:
O157.5
摘要:
设Tn为n个顶点的树的集合.Hofmeister已经对Tn的最大特征值进行了排序,给出了第1至第5位的序及它们所对应的树,常安给出第6至第8位的序,梁修东确定了第9位的值及对应的树.本文主要讨论了树的最大特征值的上界,并确定了第10位的值及对应的树.
Abstract:
LetTn be a set o f trees w ith n ve rtices. H ofme ister has determ ined the first to the fifth va lues o f the largest e-i genva lue o f trees in Tn and the correspond ing trees for these va lues. ChangAn has de term ined the six th to the eighth va-l ues o f the largest e igenva lue in Tn. Liang Xiudong has de term ined the ninth va lue of the largest eigenva lue in Tn and g iven the co rresponding tree. Th is paper studied the uppe r bound of the largest e ig envalue of trees, and determ ined the ten th va lue of the largest e igenv alue in Tn and present the corresponding tree.

参考文献/References:

[ 1] Bondy J A, Murty U S R. G raph TheoryW ith App lica tions[M ] . New Yo rk: London and E lserv ier, 1976.
[ 2] No rm an B igg s. A lgebra ic Graph Theory [M ]. Cambr idge: Cambr idge Un iversity Press, 1993.
[ 3] H ofm eisterM. On the two largest e ig envalues of trees[ J]. Linear A lgebra and its Applications, 1997, 260: 43-59.
[ 4] 李乔, 冯克勤. 论图的最大特征根[ J]. 应用数学学报, 1979, 4( 2): 167-175.
[ 5] An Chang, Huang Q iongx iang. Order ing trees by the ir largest e igenva lues[ J]. L inear A lgebra and its App lications, 2003, 370: 175-184.
[ 6] Shao J Y. Bounds on theK th e ignevalue o f trees and forests[ J]. L inear A lgebra and its Applica tions, 1991, 149: 19-34.
[ 7] 梁修东. 树的最大特征值的序[ J]. 江南大学学报: 自然科学版, 2007, 12( 5): 627-630.
[ 8] Cvetkov ic D, DoobM, SachsH. Spectra of G raph-Theory and Application[M ]. New Yo rk: Academ ic Press, 1980.
[ 9] An Chang. On the largest e igenva lue of a treew ith perfect m atchings[ J] . D iscreteM athem atics, 2003, 269: 45-63.

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备注/Memo

备注/Memo:
基金项目: 国家自然科学基金( 61003224)、中央高校基本科研业务费专项资金( 2009B21414) . 通讯联系人: 徐新萍, 博士, 教授, 研究方向: 图论与组合. E-mail: xxp3268@ sina. Com
更新日期/Last Update: 2013-04-08