On Metric Dimension in Some Hex Derived Networks

Zehui Shao; Pu Wu; Enqiang Zhu; Lanxiang Chen

doi:10.3390/s19010094

On Metric Dimension in Some Hex Derived Networks

Sensors (Basel). 2018 Dec 28;19(1):94. doi: 10.3390/s19010094.

Authors

Zehui Shao¹, Pu Wu², Enqiang Zhu³, Lanxiang Chen⁴

Affiliations

¹ Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China. zshao@gzhu.edu.cn.
² Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China. puwu1997@126.com.
³ Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China. zhuenqiang@pku.edu.cn.
⁴ College of Mathematics and Informatics, Fujian Normal University, Fujian Provincial Key Laboratory of Network Security and Cryptology, Fujian Network & Information Security Industry Technology Development Base, Fuzhou 350117, China. lxiangchen@fjnu.edu.cn.

Abstract

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 m d ( 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 m d ( H D N 1 ( 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.

Keywords: metric basis; metric dimension; robot navigation; sensor network.