A graph discretization of vector Laplacian

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-09-23 DOI:10.1016/j.dam.2025.09.019

Shu Li , Lu Lu , Jianfeng Wang

引用次数: 0

Abstract

As known, the scalar Laplacian gives the celebrated Laplacian matrix of a graph. In this paper, we determine the graph matrix presentation of vector Laplacian (or Helmholtz operator), named as Helmholtzian matrix. To compare the difference and similarity with previous graph matrices, we study the limit points of spectral radius and characterize the connected graphs with spectral radius at most 4.38+ via Helmholtzian matrix. Finally, we discuss the potential applications of Helmholtzian spectra of graphs in the simplicial networks and small-world networks.

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向量拉普拉斯的图离散化

众所周知，标量拉普拉斯矩阵给出了著名的图的拉普拉斯矩阵。本文确定了向量拉普拉斯算子（或亥姆霍兹算子）的图矩阵表示形式，称为亥姆霍兹矩阵。为了比较与以往图矩阵的异同，我们研究了谱半径的极限点，并利用Helmholtzian矩阵对谱半径不超过4.38+的连通图进行了表征。最后讨论了图的Helmholtzian谱在简单网络和小世界网络中的潜在应用。

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

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.