Knodel图的2次支配数及其在通信网络中的应用

IF 1.8 4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
R. Sundara Rajan, Arulanand S, S. Prabhu, Indra Rajasingh
{"title":"Knodel图的2次支配数及其在通信网络中的应用","authors":"R. Sundara Rajan, Arulanand S, S. Prabhu, Indra Rajasingh","doi":"10.1051/ro/2023173","DOIUrl":null,"url":null,"abstract":"In a graph G, if each node v∈V (G)\\S is connected to some node in S, then the set S of nodes is referred to as a dominating set. The domination number of G is the minimum cardinality of all dominating sets of G and is represented by γ(G). If a dominating set S monitors every node in the system under a set of guidelines for power systems monitoring, then the set S is referred to as a power-dominating set of G. The power domination number of G is the least number of vertices of a power dominating set of G. A generalization of power domination is the k-power domination in a graph G. The k-power domination number of G is the minimum cardinality of all k-power dominating sets of G and is represented by γp,k(G). In this paper, we have obtained the 2-power domination number represented by γp,2(G) for 4-regular Kn¨odel graphs and given the lower bound for 5-regular Kn¨odel graphs.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"34 16","pages":"0"},"PeriodicalIF":1.8000,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"2-power domination number for Knodel graphs and its application in communication networks\",\"authors\":\"R. Sundara Rajan, Arulanand S, S. Prabhu, Indra Rajasingh\",\"doi\":\"10.1051/ro/2023173\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a graph G, if each node v∈V (G)\\\\S is connected to some node in S, then the set S of nodes is referred to as a dominating set. The domination number of G is the minimum cardinality of all dominating sets of G and is represented by γ(G). If a dominating set S monitors every node in the system under a set of guidelines for power systems monitoring, then the set S is referred to as a power-dominating set of G. The power domination number of G is the least number of vertices of a power dominating set of G. A generalization of power domination is the k-power domination in a graph G. The k-power domination number of G is the minimum cardinality of all k-power dominating sets of G and is represented by γp,k(G). In this paper, we have obtained the 2-power domination number represented by γp,2(G) for 4-regular Kn¨odel graphs and given the lower bound for 5-regular Kn¨odel graphs.\",\"PeriodicalId\":54509,\"journal\":{\"name\":\"Rairo-Operations Research\",\"volume\":\"34 16\",\"pages\":\"0\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rairo-Operations Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/ro/2023173\",\"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/2023173","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: 0

摘要

在图G中,如果每个节点v∈v (G)\S与S中的某个节点相连,则将节点的集合S称为支配集。G的支配数是G的所有支配集的最小基数,用γ(G)表示。如果支配集S监控系统下一组中的每个节点电力系统监测指南,然后集合S称为power-dominating组G G的权力支配数量最少的顶点的权力支配组G .泛化的权力统治是k次方统治图G·k次方统治的G的最低基数是所有k次方G和支配集是由γp k (G)。本文给出了4正则Kn型图的2次方支配数γp,2(G),并给出了5正则Kn型图的下界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
2-power domination number for Knodel graphs and its application in communication networks
In a graph G, if each node v∈V (G)\S is connected to some node in S, then the set S of nodes is referred to as a dominating set. The domination number of G is the minimum cardinality of all dominating sets of G and is represented by γ(G). If a dominating set S monitors every node in the system under a set of guidelines for power systems monitoring, then the set S is referred to as a power-dominating set of G. The power domination number of G is the least number of vertices of a power dominating set of G. A generalization of power domination is the k-power domination in a graph G. The k-power domination number of G is the minimum cardinality of all k-power dominating sets of G and is represented by γp,k(G). In this paper, we have obtained the 2-power domination number represented by γp,2(G) for 4-regular Kn¨odel graphs and given the lower bound for 5-regular Kn¨odel graphs.
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
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.
×
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