Unicyclic graphs and the inertia of the squared distance matrix

IF 0.7 4区 数学 Q2 Mathematics
Christian Howell, Mark Kempton, Kellon Sandall, John Sinkovic
{"title":"Unicyclic graphs and the inertia of the squared distance matrix","authors":"Christian Howell, Mark Kempton, Kellon Sandall, John Sinkovic","doi":"10.13001/ela.2023.7543","DOIUrl":null,"url":null,"abstract":"A result of Bapat and Sivasubramanian gives the inertia of the squared distance matrix of a tree. We develop general tools on how pendant vertices and vertices of degree 2 affect the inertia of the squared distance matrix and use these to give an alternative proof of this result. We further use these tools to extend this result to certain families of unicyclic graphs, and we explore how far these results can be extended.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":"11 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13001/ela.2023.7543","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1

Abstract

A result of Bapat and Sivasubramanian gives the inertia of the squared distance matrix of a tree. We develop general tools on how pendant vertices and vertices of degree 2 affect the inertia of the squared distance matrix and use these to give an alternative proof of this result. We further use these tools to extend this result to certain families of unicyclic graphs, and we explore how far these results can be extended.
单环图和距离平方矩阵的惯性
Bapat和Sivasubramanian的结果给出了树的距离平方矩阵的惯性。我们开发了一些通用的工具来说明垂顶点和2次顶点是如何影响距离平方矩阵的惯性的,并用这些工具来给出这个结果的另一种证明。我们进一步使用这些工具将这个结果扩展到某些单环图族,并探索这些结果可以扩展到什么程度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信