{"title":"最小化有符号完整图的最小拉普拉奇特征值","authors":"Dan Li, Minghui Yan, Jixiang Meng","doi":"10.1016/j.amc.2024.129002","DOIUrl":null,"url":null,"abstract":"<div><p>A signed graph Σ is a graph whose edges yield the signs ±1. Let <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be the complete graph with <em>n</em> vertices and <span><math><mi>Σ</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span> be a signed complete graph, where <em>F</em> is a subgraph induced by the negative edges of Σ. The least Laplacian eigenvalue of Σ is the least eigenvalue of its Laplacian matrix. A unicyclic graph is a connected graph containing exactly one cycle. In this paper, we focus on the least Laplacian eigenvalue of <span><math><mi>Σ</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span>, where <em>F</em> is a unicyclic graph.</p></div>","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0096300324004636/pdfft?md5=f575acb8362aad3fa0b606f548e03842&pid=1-s2.0-S0096300324004636-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Minimizing the least Laplacian eigenvalue of signed complete graphs\",\"authors\":\"Dan Li, Minghui Yan, Jixiang Meng\",\"doi\":\"10.1016/j.amc.2024.129002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A signed graph Σ is a graph whose edges yield the signs ±1. Let <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be the complete graph with <em>n</em> vertices and <span><math><mi>Σ</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span> be a signed complete graph, where <em>F</em> is a subgraph induced by the negative edges of Σ. The least Laplacian eigenvalue of Σ is the least eigenvalue of its Laplacian matrix. A unicyclic graph is a connected graph containing exactly one cycle. In this paper, we focus on the least Laplacian eigenvalue of <span><math><mi>Σ</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span>, where <em>F</em> is a unicyclic graph.</p></div>\",\"PeriodicalId\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0096300324004636/pdfft?md5=f575acb8362aad3fa0b606f548e03842&pid=1-s2.0-S0096300324004636-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300324004636\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324004636","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
摘要
有符号图 Σ 是一个图，其边的符号为 ±1。 设 Kn 是有 n 个顶点的完整图，Σ=(Kn,F-) 是一个有符号的完整图，其中 F 是由Σ 的负边引起的子图。Σ 的最小拉普拉斯特征值是其拉普拉斯矩阵的最小特征值。单循环图是指包含一个循环的连通图。本文重点研究 Σ=(Kn,F-) 的最小拉普拉奇特征值，其中 F 是单环图。
Minimizing the least Laplacian eigenvalue of signed complete graphs
A signed graph Σ is a graph whose edges yield the signs ±1. Let be the complete graph with n vertices and be a signed complete graph, where F is a subgraph induced by the negative edges of Σ. The least Laplacian eigenvalue of Σ is the least eigenvalue of its Laplacian matrix. A unicyclic graph is a connected graph containing exactly one cycle. In this paper, we focus on the least Laplacian eigenvalue of , where F is a unicyclic graph.
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