New Bounds for Codes Identifying Vertices in Graphs

Let G = (V, E) be an undirected graph. Let C be a subset of vertices that we shall call a code. For any vertex v V , the neighbouring set N(v, C) is the set of vertices of C at distance at most one from v. We say that the code C identifies the vertices of G if the neighbouring sets N(v, C), v V, are all nonempty and different. What is the smallest size of an identifying code C ? We focus on the case when G is the two-dimensional square lattice and improve previous upper and lower bounds on the minimum size of such a code. AMS subject classification: 05C70, 68R10, 94B99, 94C12. Submitted: February 12, 1999; Accepted: March 15, 1999. G. Cohen, A. Lobstein and G. Z

• Type: Journal
• Year: 1999
• Where: COMBINATORICS
• Authors: Gérard D. Cohen, Iiro S. Honkala, Antoine Lobstein, Gilles Zémor
• Keywords: Code, COMBINATORICS 1999, Two-dimensional Square Lattice, Undirected Graph