An optimal strongly identifying code in the infinite triangular grid

Abstract

Assume that G = (V, E) is an undirected graph, and C subset of V. For every v is an element of V, we denote by I(v) the set of all elements of C that are within distance one from v. If the sets I(v){v} for v is an element of V are all nonempty, and, moreover, the sets {I(v), I(v){v}} for v is an element of V are disjoint, then C is called a strongly identifying code. The smallest possible density of a strongly identifying code in the infinite triangular grid is shown to be 6/19.