Landmarks in torus networks
Paul D Manuel, Bharati Rajan, Indra Rajasingh, M. Chris Monica · Journal of Discrete Mathematical Sciences and Cryptography · 2006
A minimum metric basis is a minimum set M of vertices of a graph G(V, E) such that for every pair of vertices u and v of V\M, there exists a vertex w∈M 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. In this paper we study the minimum metric dimension problem for torus networks. We prove that for torus TR(m, n), m≤n, the minimum metric dimension is 3 when at least one of m or n is odd. We provide an upper bound for the minimum metric dimension when both m and n are even.