An Optimal Strongly Identifying Code in the Infinite Triangular Grid

Assume that G = (V,E) is an undirected graph, and C ⊆ V . For every v ∈ 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 ∈ V are all nonempty, and, moreover, the sets {I(v), I(v) \ {v}} for v ∈ 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.