Bounds on identifying codes

Improved bounds on identifying codes in binary Hamming spaces

General Bounds for Identifying Codes in Some Infinite Regular Graphs

Consider a connected undirected graph G = (V,E) and a subset of vertices C. If for all vertices v ∈ V , the sets Br(v) ∩ C are all nonempty and pairwise distinct, where Br(v) denotes the set of all points within distance r from v, then we call C an r-identifying code. We give general lower and upper bounds on the best possible density of r-identifying codes in three infinite regular graphs.

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 th...

Bounds for Identifying Codes in Terms of Degree Parameters

An identifying code is a subset of vertices of a graph such that each vertex is uniquely determined by its neighbourhood within the identifying code. If γ(G) denotes the minimum size of an identifying code of a graph G, it was conjectured by F. Foucaud, R. Klasing, A. Kosowski and A. Raspaud that if a connected graph G has n vertices and maximum degree d and admits an identifying code, then γ(G...

Bounds for Codes Identifying Vertices in the Hexagonal Grid

In an undirected graph G = (V; E) a subset C V is called an identifying code, if the sets B1 (v) \ C consisting of all elements of C within distance one from the vertex v are nonempty and diierent. We take G to be the innnite hexagonal grid, and show that the density of any identifying code is at least 16=39 and that there is an identifying code of density 3=7.