Metric Dimension and Robot Navigation in Specific Sensor Networks
Zehui Shao, Pu Wu, Enqiang Zhu, Lanxiang Chen · 2018
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.