New conjectures on algebraic connectivity and the Laplacian spread of graphs

被引：4

作者：

Barrett, Wayne ^{[1
]}

Evans, Emily ^{[1
]}

Hall, H. Tracy ^{[2
]}

Kempton, Mark ^{[1
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT USA

[2] Hall Labs LLC, Provo, UT USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2022年 / 648卷

关键词：

Laplacian; Eigenvalue; Laplacian spread conjecture; Algebraic connectivity; Eccentricity;

D O I：

10.1016/j.laa.2022.04.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implies a strengthening of the Laplacian Spread Conjecture. We discuss further conjectures, also strengthening the Laplacian Spread Conjecture, that include a conjecture for simple graphs and a conjecture for weighted graphs. (c) 2022 Elsevier Inc. All rights reserved.

引用

页码：104 / 132

页数：29

共 9 条

[1] The algebraic connectivity of a graph and its complement [J].