a α-特征值的界

IF 1.8 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Rairo-Operations Research Pub Date : 2023-09-11 DOI:10.1051/ro/2023144

João Domingos Gomes da Silva Júnior, Carla Silva Oliveira, Liliana Manuela G. C. da Costa

{"title":"a α-特征值的界","authors":"João Domingos Gomes da Silva Júnior, Carla Silva Oliveira, Liliana Manuela G. C. da Costa","doi":"10.1051/ro/2023144","DOIUrl":null,"url":null,"abstract":"Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] defined the matrix Aα(G), as a convex combination of A(G) and D(G), the following way, Aα(G) = αA(G) + (1 − α)D(G), where α ∈ [0,1]. In this paper we present some new upper and lower bounds for the largest, second largest and the smallest eigenvalue of Aα-matrix. Moreover, extremal graphs attaining some of these bounds are characterized.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"27 1","pages":"0"},"PeriodicalIF":1.8000,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Bounds for Aα-eigenvalues\",\"authors\":\"João Domingos Gomes da Silva Júnior, Carla Silva Oliveira, Liliana Manuela G. C. da Costa\",\"doi\":\"10.1051/ro/2023144\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] defined the matrix Aα(G), as a convex combination of A(G) and D(G), the following way, Aα(G) = αA(G) + (1 − α)D(G), where α ∈ [0,1]. In this paper we present some new upper and lower bounds for the largest, second largest and the smallest eigenvalue of Aα-matrix. Moreover, extremal graphs attaining some of these bounds are characterized.\",\"PeriodicalId\":54509,\"journal\":{\"name\":\"Rairo-Operations Research\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rairo-Operations Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/ro/2023144\",\"RegionNum\":4,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rairo-Operations Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/ro/2023144","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}

引用次数: 1

摘要

设G为具有邻接矩阵a (G)和度对角矩阵D(G)的图。2017年，Nikiforov[1]将矩阵a α(G)定义为a (G)与D(G)的凸组合，即a α(G) = α a (G) +(1−α)D(G)，其中α∈[0,1]。本文给出了a α-矩阵的最大、第二大和最小特征值的一些新的上界和下界。此外，对达到某些边界的极值图进行了刻画。

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

Bounds for Aα-eigenvalues

Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] defined the matrix Aα(G), as a convex combination of A(G) and D(G), the following way, Aα(G) = αA(G) + (1 − α)D(G), where α ∈ [0,1]. In this paper we present some new upper and lower bounds for the largest, second largest and the smallest eigenvalue of Aα-matrix. Moreover, extremal graphs attaining some of these bounds are characterized.

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

Rairo-Operations Research 管理科学-运筹学与管理科学

CiteScore

3.60

自引率

22.20%

发文量

206

审稿时长

>12 weeks

期刊介绍： RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.