On Metric Dimension in Some Hex Derived Networks

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 <i>G</i> is the smallest number <i>k</i> for which <i>G</i> contains a vertex set <i>W</i>, such that | W | = k and every pair of vertices of <i>G</i> possess different distances to at least one vertex in <i>W</i>. 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.