On minimum metric dimension of honeycomb networks

Abstract

A minimum metric basis is a minimum set W of vertices of a graph G ( V , E ) such that for every pair of vertices u and v of G, there exists a vertex w ∈ W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. The honeycomb and hexagonal networks are popular mesh-derived parallel architectures. Using the duality of these networks we determine minimum metric bases for hexagonal and honeycomb networks.