An explicit upper bound on disparity for trees of a given diameter

被引：0

作者：

Cinzori, Isaac ^{[1
]}

Johnson, Charles R. ^{[2
]}

Lang, Hannah ^{[3
]}

机构：

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23185 USA

[3] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 19期

基金：

美国国家科学基金会;

关键词：

Branch duplication; distinct eigenvalues; graph of a matrix; seed; rooted seed;

D O I：

10.1080/03081087.2021.1887070

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that the minimum number of distinct eigenvalues c(T) of a symmetric matrix whose graph is a given tree T is at least the diameter d(T) of that tree. However, the disparity c(T) - d(T) can be positive. Using branch duplication and rooted seeds, the notion of the `most complex seed' is introduced, and an explicit upper bound on the disparity is given for any tree of a given diameter.

引用

页码：4584 / 4596

页数：13

共 4 条

[1] Diameter minimal trees
Johnson, Charles R.
Saiago, Carlos M.
LINEAR & MULTILINEAR ALGEBRA, 2016, 64 (03) : 557 - 571
[2] UPPER BOUND FOR THE NUMBER OF DISTINCT EIGENVALUES OF A PERTURBED MATRIX
Moon, Sunyo
Park, Seungkook
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2018, 34 : 115 - 124
[3] Growth allocation between height and stem diameter in nonsuppressed reproducing Abies mariesii trees
Seki, Takeshi
Ohta, Sadaaki
Fujiwara, Takeshi
Nakashizuka, Tohru
PLANT SPECIES BIOLOGY, 2013, 28 (02) : 146 - 155
[4] An improved upper bound for the number of distinct eigenvalues of a matrix after perturbation
Xu, Xuefeng
LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 523 : 109 - 117

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