{"title":"Metric Dimension and Robot Navigation in Specific Sensor Networks","authors":"Z. Shao, Pu Wu, Enqiang Zhu, Lanxiang Chen","doi":"10.1109/CYBERC.2018.00072","DOIUrl":null,"url":null,"abstract":"The concept of metric dimension was proposed to model robot navigation where the places of navigating agents can change among nodes. The metric dimension md(G) of a graph G is the smallest number k for which G contains a vertex set W such that |W| = k and every pair of vertices of G possess different distances to at least one vertex in W. In this paper, we demonstrate that md(HDN1(n)) = 4 for n ≥ 2, this indicates that in this type of hex derived sensor networks, the least number of nodes needed is 4 for locating any other node in such a sensor network.","PeriodicalId":282903,"journal":{"name":"2018 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CYBERC.2018.00072","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
The concept of metric dimension was proposed to model robot navigation where the places of navigating agents can change among nodes. The metric dimension md(G) of a graph G is the smallest number k for which G contains a vertex set W such that |W| = k and every pair of vertices of G possess different distances to at least one vertex in W. In this paper, we demonstrate that md(HDN1(n)) = 4 for n ≥ 2, this indicates that in this type of hex derived sensor networks, the least number of nodes needed is 4 for locating any other node in such a sensor network.
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