论外平面图的展开

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2021-11-23 DOI:10.1515/spma-2022-0164

D. Gotshall, M. O’Brien, Michael Tait

{"title":"论外平面图的展开","authors":"D. Gotshall, M. O’Brien, Michael Tait","doi":"10.1515/spma-2022-0164","DOIUrl":null,"url":null,"abstract":"Abstract The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n)\\Omega \\left(n) edges. We conjecture that the extremal graph is a vertex joined to a path on n−1n-1 vertices.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"299 - 307"},"PeriodicalIF":0.8000,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the spread of outerplanar graphs\",\"authors\":\"D. Gotshall, M. O’Brien, Michael Tait\",\"doi\":\"10.1515/spma-2022-0164\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n)\\\\Omega \\\\left(n) edges. We conjecture that the extremal graph is a vertex joined to a path on n−1n-1 vertices.\",\"PeriodicalId\":43276,\"journal\":{\"name\":\"Special Matrices\",\"volume\":\"10 1\",\"pages\":\"299 - 307\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-11-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Special Matrices\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/spma-2022-0164\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Special Matrices","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/spma-2022-0164","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

图的展开是其邻接矩阵的最大和最负特征值之间的差。我们证明了对于足够大的nn，具有最大展开的nn顶点外平面图是连接到具有Ω（n）\Omega\left（n）边的线性森林的顶点。我们猜想极值图是一个连接到n−1n-1个顶点上的路径的顶点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the spread of outerplanar graphs

Abstract The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n)\Omega \left(n) edges. We conjecture that the extremal graph is a vertex joined to a path on n−1n-1 vertices.

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

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.