{"title":"Monitoring Edge-Geodetic Numbers of Mycielskian Graph Classes","authors":"Xin Li, Wen Li, Ao Tan, Mengmeng He, Weizhen Chen","doi":"10.1142/s0219265924500105","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] be a graph and [Formula: see text] be the vertex set of [Formula: see text]. If any edge appears in the unique shortest path of at least one vertex pair in set [Formula: see text], then [Formula: see text] is defined as the monitoring edge-geodetic set (MEG-set for short). We denote by [Formula: see text] the size of a smallest MEG-set of [Formula: see text]. In this paper, we studied the monitoring edge-geodetic numbers of Mycielski graph classes.","PeriodicalId":53990,"journal":{"name":"JOURNAL OF INTERCONNECTION NETWORKS","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-05-23","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/s0219265924500105","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
Abstract
Let [Formula: see text] be a graph and [Formula: see text] be the vertex set of [Formula: see text]. If any edge appears in the unique shortest path of at least one vertex pair in set [Formula: see text], then [Formula: see text] is defined as the monitoring edge-geodetic set (MEG-set for short). We denote by [Formula: see text] the size of a smallest MEG-set of [Formula: see text]. In this paper, we studied the monitoring edge-geodetic numbers of Mycielski graph classes.
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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