On the distance spectra of graphs

被引：27

作者：

Aalipour, Ghodratollah ^{[1
,2
]}

Abiad, Aida ^{[3
]}

Berikkyzy, Zhanar ^{[4
]}

Cummings, Jay ^{[5
]}

De Silva, Jessica ^{[6
]}

Gao, Wei ^{[7
]}

Heysse, Kristin ^{[4
]}

Hogben, Leslie ^{[4
,8
]}

Kenter, Franklin H. J. ^{[9
]}

Lin, Jephian C. -H. ^{[4
]}

Tait, Michael ^{[5
]}

机构：

[1] Kharazmi Univ, Dept Math & Comp Sci, 50 Taleghani St, Tehran, Iran

[2] Univ Colorado Denver, Dept Math & Stat Sci, Denver, CO USA

[3] Maastricht Univ, Dept Quantitat Econ, Operat Res, NL-6200 MD Maastricht, Netherlands

[4] Iowa State Univ, Dept Math, Ames, IA 50011 USA

[5] Univ Calif San Diego, Dept Math, La Jolla, CA 92037 USA

[6] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[7] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

[8] Amer Inst Math, 600 E Brokaw Rd, San Jose, CA 95112 USA

[9] Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 497卷

基金：

美国国家科学基金会;

关键词：

Distance matrix; Eigenvalue; Distance regular graph; Kneser graph; Double odd graph; Doob graph; Lollipop graph; Barbell graph; Distance spectrum; Strongly regular graph; Optimistic graph; Determinant; Inertia; Graph; MATRIX;

D O I：

10.1016/j.laa.2016.02.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The distance matrix of a graph G is the matrix containing the pairwise distances between vertices. The distance eigenvalues of G are the eigenvalues of its distance matrix and they form the distance spectrum of G. We determine the distance spectra of double odd graphs and Doob graphs, completing the determination of distance spectra of distance regular graphs having exactly one positive distance eigenvalue. We characterize strongly regular graphs having more positive than negative distance eigenvalues. We give examples of graphs with few distinct distance eigenvalues but lacking regularity properties. We also determine the determinant and inertia of the distance matrices of lollipop and barbell graphs. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：66 / 87

页数：22

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