On Metric Dimension in Some Hex Derived Networks

被引：19
作者：
Shao, Zehui [1 ]
Wu, Pu [1 ]
Zhu, Enqiang [1 ]
Chen, Lanxiang [2 ]
机构：
[1] Guangzhou Univ, Inst Comp Sci & Technol, Guangzhou 510006, Guangdong, Peoples R China
[2] Fujian Normal Univ, Fujian Prov Key Lab Network Secur & Cryptol, Fujian Network & Informat Secur Ind Technol Dev B, Coll Math & Informat, Fuzhou 350117, Fujian, Peoples R China
来源：
SENSORS | 2019年 / 19卷 / 01期
关键词：
robot navigation; sensor network; metric dimension; metric basis; HONEYCOMB; GRAPHS;
D O I：
10.3390/s19010094
中图分类号：
O65 [分析化学];
学科分类号：
070302 ; 081704 ;
摘要：
The concept of a 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 vertical bar W vertical bar = 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 these types of hex derived sensor networks, the least number of nodes needed for locating any other node is four.
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页数：9
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