A unified framework for the Expander Mixing Lemma for irregular graphs and its applications

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-08-02 DOI:10.1016/j.laa.2024.07.023

Aida Abiad, Sjanne Zeijlemaker

引用次数: 0

Abstract

A unified framework for the Expander Mixing Lemma for irregular graphs using adjacency eigenvalues is presented, as well as two new versions of it. While the existing Expander Mixing Lemmas for irregular graphs make use of the notion of volume (the sum of degrees within a vertex set), we instead propose to use the Perron eigenvector entries as vertex weights, which is a way to regularize the graph. This provides a new application of weight partitions of graphs. The new Expander Mixing Lemma versions are then applied to obtain several eigenvalue bounds for NP-hard parameters such as the zero forcing number, the vertex integrity and the routing number of a graph.

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不规则图的扩展混合定理及其应用的统一框架

本文提出了使用邻接特征值的不规则图扩展混合定理的统一框架以及两个新版本。现有的不规则图扩展混合定理使用的是体积概念（顶点集合内的度数总和），而我们建议使用佩伦特征向量项作为顶点权重，这是一种使图规则化的方法。这为图的权重分区提供了一种新的应用。然后，我们应用新的扩展混合谬误版本，为 NP 难参数（如图的零强制数、顶点完整性和路由数）获得了几个特征值边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.