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 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 these types of hex derived sensor networks, the least number of nodes needed for locating any other node is four.