关于steinberger曲率和图距离矩阵

IF 0.7 3区数学 Q2 MATHEMATICS Discrete Mathematics Pub Date : 2025-08-01 Epub Date: 2025-03-07 DOI:10.1016/j.disc.2025.114475

Wei-Chia Chen , Mao-Pei Tsui

{"title":"关于steinberger曲率和图距离矩阵","authors":"Wei-Chia Chen , Mao-Pei Tsui","doi":"10.1016/j.disc.2025.114475","DOIUrl":null,"url":null,"abstract":"<div><div>Steinerberger proposed a notion of curvature on graphs involving the graph distance matrix (J. Graph Theory, 2023). We show that nonnegative curvature is almost preserved under three graph operations. We characterize the distance matrix and its null space after adding an edge between two graphs. Let <em>D</em> be the graph distance matrix and <strong>1</strong> be the all-one vector. We provide a way to construct graphs so that the linear system <span><math><mi>D</mi><mi>x</mi><mo>=</mo><mn>1</mn></math></span> does not have a solution.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 8","pages":"Article 114475"},"PeriodicalIF":0.7000,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Steinerberger curvature and graph distance matrices\",\"authors\":\"Wei-Chia Chen , Mao-Pei Tsui\",\"doi\":\"10.1016/j.disc.2025.114475\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Steinerberger proposed a notion of curvature on graphs involving the graph distance matrix (J. Graph Theory, 2023). We show that nonnegative curvature is almost preserved under three graph operations. We characterize the distance matrix and its null space after adding an edge between two graphs. Let <em>D</em> be the graph distance matrix and <strong>1</strong> be the all-one vector. We provide a way to construct graphs so that the linear system <span><math><mi>D</mi><mi>x</mi><mo>=</mo><mn>1</mn></math></span> does not have a solution.</div></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":\"348 8\",\"pages\":\"Article 114475\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X25000834\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/3/7 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X25000834","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/7 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

Steinerberger提出了涉及图距离矩阵的图上曲率的概念（J. graph Theory, 2023）。我们证明了非负曲率在三种图运算下几乎保持不变。在两个图之间添加一条边后，我们描述了距离矩阵及其零空间。设D为图距离矩阵，1为全向量。我们提供了一种构造图形的方法，使得线性方程组Dx=1没有解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On Steinerberger curvature and graph distance matrices

Steinerberger proposed a notion of curvature on graphs involving the graph distance matrix (J. Graph Theory, 2023). We show that nonnegative curvature is almost preserved under three graph operations. We characterize the distance matrix and its null space after adding an edge between two graphs. Let D be the graph distance matrix and 1 be the all-one vector. We provide a way to construct graphs so that the linear system

D x = 1

does not have a solution.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.

期刊最新文献

Paradoxical behavior in Collatz sequences The defective parking space and defective Kreweras numbers The spectral moments of hypertrees and unicyclic hypergraphs Spectral radius and Hamiltonicity of uniform hypergraphs Generalized matching extension problem in regular bipartite graphs