Optimal t-Edge-Robust r-Identifying Codes in the King Lattice
Graphs and Combinatorics
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
On robust and dynamic identifying codes
IEEE Transactions on Information Theory
On identifying codes that are robust against edge changes
Information and Computation
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Assume that G = (V, E) is a simple undirected graph, and C is a nonempty subset of V. For every v ∈ V, we denote lr(v) = {u ∈ C | dG(u, v) ≤ r}, where dG(u, v) denotes the number of edges on any shortest path between u and v. If the sets lr(v) for v ∈ V are pairwise different, and none of them is the empty set, we say that C is an r-identifying code in G. If C is r-identifying in every graph G' that can be obtained by adding and deleting edges in such a way that the number of additions and deletions together is at most t, the code C is called t-edge-robust. Let K be the graph with vertex set Z2 in which two different vertices are adjacent if their Euclidean distance is at most √2. We show that the smallest possible density of a 3-edge-robust code in K is r+1/2r+1 for all r 2.