Metric Dimension and Robot Navigation in Specific Sensor Networks

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.