{"title":"监测某些网络的边缘大地数字","authors":"Yingying Zhang, Fanfan Wang, Chenxu Yang","doi":"10.1142/s0219265924500014","DOIUrl":null,"url":null,"abstract":"Motivated by the problem of network monitoring, Foucaud, Krishna and Ramasubramony Sulochana introduced the concept of monitoring edge-geodetic set and a related graph invariant. A monitoring edge-geodetic set (MEG-set for short) is a set such that the removal of any edge changes the distance between some pair of vertices in the set. The minimum size of the monitoring edge-geodetic set is called the monitoring edge-geodetic number. In this paper, we study the monitoring edge-geodetic numbers of some well-known networks, including folded hypercube, folded [Formula: see text]-cube, prism graph, anti-prism graph, Jahangir graph and windmill graphs.","PeriodicalId":53990,"journal":{"name":"JOURNAL OF INTERCONNECTION NETWORKS","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Monitoring Edge-Geodetic Numbers of Some Networks\",\"authors\":\"Yingying Zhang, Fanfan Wang, Chenxu Yang\",\"doi\":\"10.1142/s0219265924500014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by the problem of network monitoring, Foucaud, Krishna and Ramasubramony Sulochana introduced the concept of monitoring edge-geodetic set and a related graph invariant. A monitoring edge-geodetic set (MEG-set for short) is a set such that the removal of any edge changes the distance between some pair of vertices in the set. The minimum size of the monitoring edge-geodetic set is called the monitoring edge-geodetic number. In this paper, we study the monitoring edge-geodetic numbers of some well-known networks, including folded hypercube, folded [Formula: see text]-cube, prism graph, anti-prism graph, Jahangir graph and windmill graphs.\",\"PeriodicalId\":53990,\"journal\":{\"name\":\"JOURNAL OF INTERCONNECTION NETWORKS\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JOURNAL OF INTERCONNECTION NETWORKS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219265924500014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF INTERCONNECTION NETWORKS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219265924500014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
摘要
受网络监控问题的启发，Foucaud、Krishna 和 Ramasubramony Sulochana 提出了监控边-大地集的概念和相关的图不变式。监控边-大地集（简称 MEG 集）是这样一个集合：移除任何一条边都会改变集合中某对顶点之间的距离。监测边-大地集的最小大小称为监测边-大地数。本文研究了一些著名网络的监测边几何数，包括折叠超立方图、折叠[公式：见正文]立方图、棱柱图、反棱柱图、贾汉吉尔图和风车图。
Motivated by the problem of network monitoring, Foucaud, Krishna and Ramasubramony Sulochana introduced the concept of monitoring edge-geodetic set and a related graph invariant. A monitoring edge-geodetic set (MEG-set for short) is a set such that the removal of any edge changes the distance between some pair of vertices in the set. The minimum size of the monitoring edge-geodetic set is called the monitoring edge-geodetic number. In this paper, we study the monitoring edge-geodetic numbers of some well-known networks, including folded hypercube, folded [Formula: see text]-cube, prism graph, anti-prism graph, Jahangir graph and windmill graphs.
期刊介绍：
The Journal of Interconnection Networks (JOIN) is an international scientific journal dedicated to advancing the state-of-the-art of interconnection networks. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks. Interconnection problems occur at different levels in the hardware and software design of communicating entities in integrated circuits, multiprocessors, multicomputers, and communication networks as diverse as telephone systems, cable network systems, computer networks, mobile communication networks, satellite network systems, the Internet and biological systems.
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