On the Laplacian spread of digraphs

被引：0

作者：

Barrett, Wayne ^{[1
]}

Cameron, Thomas R. ^{[2
]}

Evans, Emily ^{[1
]}

Hall, H. Tracy ^{[3
]}

Kempton, Mark ^{[1
]}

机构：

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

[2] Penn State Behrend, Dept Math, Erie, PA 16802 USA

[3] Hall Labs LLC, Provo, UT USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 664卷

关键词：

Numerical range; Directed graph; Laplacian matrix; Laplacian spread; Algebraic connectivity; ALGEBRAIC CONNECTIVITY; GRAPH; RANGE;

D O I：

10.1016/j.laa.2023.01.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values for several families of digraphs. Then, we prove sharp upper bounds on the Laplacian spread for all polygonal and balanced digraphs. In particular, we show that the validity of the Laplacian spread bound for balanced digraphs is equivalent to the Laplacian spread conjecture for simple undirected graphs, which was conjectured in 2011 and proven in 2021. Moreover, we prove an equivalent statement for weighted balanced digraphs with weights between 0 and 1. Finally, we state several open conjectures that are motivated by empirical data.(c) 2023 Elsevier Inc. All rights reserved.

引用

页码：126 / 146

页数：21

共 29 条

[1] Some results on the Laplacian Spread Conjecture [J].