On strongly identifying codes

On strongly identifying codes

Identifying Codes in Vertex-Transitive Graphs and Strongly Regular Graphs

We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V |) + 1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that re...

On Dynamic Identifying Codes

A walk c1, c2, . . . , cM in an undirected graph G = (V, E) is called a dynamic identifying code, if all the sets I(v) = {u ∈ C : d(u, v) ≤ 1} for v ∈ V are nonempty and no two of them are the same set. Here d(u, v) denotes the number of edges on any shortest path from u to v, and C = {c1, c2, . . . , cM}. We consider dynamic identifying codes in square grids, triangular grids, hexagonal meshes...

1-identifying Codes on Trees

On identifying codes in lattices

Let G(V,E) be a simple, undirected graph. An identifying code on G is a vertex-subset C ⊆ V such that B(v) ∩ C is non-empty and distinct for each vertex v ∈ V , where B(v) is a ball about v. Motivated by applications to fault diagnosis in multiprocessor arrays, a number of researchers have considered the problem of constructing identifying codes of minimum density on various two-dimensional lat...